MCQ 1011 Mark
The inverse of the statement "If a person is mean, then they are a fighter" is:
- A
If a person is not mean, then they are a fighter.
- B
If a person is mean, then they are not a fighter.
- ✓
If a person is not mean, then they are not a fighter.
- D
AnswerCorrect option: C. If a person is not mean, then they are not a fighter.
A person is not mean is the negation of the hypothesis that a person is mean and they are not a fighter is the negation of the conclusion they are a fighter.
View full question & answer→MCQ 1021 Mark
Which of the following is the inverse of the proposition : “If a number is a prime then it is odd.”
- A
If a number is not a prime then it is prime
- ✓
If a number is not a prime then it is odd
- C
If a number is not odd then it is not a prime
- D
If a number is not odd then it is a prime
AnswerCorrect option: B. If a number is not a prime then it is odd
View full question & answer→MCQ 1031 Mark
Which of the following compound statement has both true component statements?
- A
A prime number is divisible by $2$ and odd
- B
Two and two makes four or five
- C
All integers are positive and divisible by $2$
- ✓
$100$ is divisible by $2$ and $5$
AnswerCorrect option: D. $100$ is divisible by $2$ and $5$
Prime number is not divisible by $2$ always.
Two and two makes our not five.
All integers are not positive.
$100$ is divisible by $2$ and $5$ both.
So, component statements of $“100$ is divisible by $2$ and $5”$ are true.
View full question & answer→MCQ 1041 Mark
Mary says "The number I am thinking is divisible by $2$ or it is divisible by $3"$. This statement is false if the number Mary is thinking of is:
AnswerThe statement is true if Mary is thinking of:
As, $6$ is divisible by both $2$ and $3.$
As, $8$ is divisible by $2.$
As, $15$ is divisible by $3.$
Hence, the statement is false for option $(C)$ as $11$ is not divisble by either $2$ or $3.$
View full question & answer→MCQ 1051 Mark
What is contrapositive for statement if $p$ then $q\ ?$
- ✓
If not $q$ then not $p$
- B
If $q$ then $p$
- C
If not $p$ then $q$
- D
If not $p$ then not $q$
AnswerCorrect option: A. If not $q$ then not $p$
Contrapositive statement for given statement “if $p$ then $q”$ is “if not $q$ then not $p”$
i.e. $\sim q \Rightarrow \sim p.$
View full question & answer→MCQ 1061 Mark
If $\text{p, q, r}$ are statement with truth vales $\text{F, T, F}$ respectively then the truth value of $p \rightarrow (q \rightarrow r)$ is.
View full question & answer→MCQ 1071 Mark
“If $p$ then $q”$ is true when $.............$
AnswerCorrect option: D. both $p \Rightarrow q$ and $q \Rightarrow p$
If $p$ then $q$ statement will be true.
If $p$ is true then $q$ must be true and if $q$ is true then $p$ must be true.
View full question & answer→MCQ 1081 Mark
Which of the following statements is the inverse of "If you do not understand geometry, then you do not know how to reason deductively."?
- ✓
If you reason deductively, then you understand geometry.
- B
If you understand geometry, then you reason deductively.
- C
If the do not reason deductively, then you understand geometry.
- D
AnswerCorrect option: A. If you reason deductively, then you understand geometry.
To find the inverse we need to negate the hypothesis and conclusion. On negating the hypothesis we get you reason deductively and on negating the conclusion we get you understand geometry.
View full question & answer→MCQ 1091 Mark
Which of the following is a statement?
- A
Women are more intelligent than men
- ✓
- C
- D
AnswerA sentence is called mathematically acceptable statement if it is either true or false but not both
“Two plus ''two is three” is false so it is a statement.
Rest we cannot decide whether they are true or false.
View full question & answer→MCQ 1101 Mark
In contrapositive method to prove statement “If $p$ then $q”$ is valid or not, we assume $p$ to be $..........$ and prove $q$ to be $..........$
AnswerIn contrapositive method, we assume $p$ to be false and use it to prove that $q$ is also false.
There is no case for $p$ to be true in direct method.
View full question & answer→MCQ 1111 Mark
If $p$ then $q$ means $..........$ implies $..........$
AnswerCorrect option: B. $\sim q \Rightarrow \sim p$
If $p$ then $q$ means $p \Rightarrow q$ or negation of $q$ implies negation of $p$
i.e. $\sim q \Rightarrow \sim p.$
View full question & answer→MCQ 1121 Mark
An analysis of the monthly wages paid to the workers of a form is given below. Calculate the total monthly wages.
|
No. of workers
|
$100$ |
|
Average monthly wages
|
$280$ |
|
Variance of distribution of wages
|
$10$ |
- A
$2800$
- B
$280$
- ✓
$28000$
- D
$2.8$
AnswerCorrect option: C. $28000$
Number of wage earners $(n_1) = 100$
Mean of monthly wages $(X_1) = ₹ 280$
Mean of monthly wages $=$ Total monthly wage/ Number of workers
$\Rightarrow 280 =\frac{\text{total monthly wages}}{100}$
$\Rightarrow \text{Total monthly}= \frac{\text{wages}} {28000}.$
View full question & answer→MCQ 1131 Mark
Choose the correct answer: Which of the following is not a statement.
AnswerTo given order cannot be a statement.
So ‘Come here’ is not a statement.
View full question & answer→MCQ 1141 Mark
If $p$ then $q$ means $..........$ is necessary condition for $..........$
- A
$p, p$
- B
$q, q$
- C
$p, q$
- ✓
$q, p$
AnswerCorrect option: D. $q, p$
If $p$ then $q$ means $q$ is necessary condition for $p$ or $p \Rightarrow q.$
It is not same as $p$ is necessary condition for $q.$
View full question & answer→MCQ 1151 Mark
The negation of the Boolean expression $\sim s ∨ (\sim r ∧ s)$ is equivalent to:
- A
$\sim s\ ∧ \sim r$
- B
$r$
- C
$s ∨ r$
- ✓
$s ∧ r$
AnswerCorrect option: D. $s ∧ r$
View full question & answer→MCQ 1161 Mark
The inverse of "If $x$ has courage, then $x$ will win", is:
- A
If $x$ will win, then $x$ has courage.
- ✓
If $x$ has no courage, then $x$ will not win.
- C
If $x$ will not win, then $x$ has no courage.
- D
If $x$ will not win, then $x$ has courage.
AnswerCorrect option: B. If $x$ has no courage, then $x$ will not win.
Take $p : x$ has courage
And $q : x$ will win
So the given conjugation is $p \Rightarrow q$
Now we need to find Inverse of this.
Be definition, Inverse of $p \Rightarrow q$ is $\sim p ⟶ \sim q$
$\sim p : x$ has no courage,
$\sim q : x$ will not win
Thus the inverse $\sim p ⟶ \sim q$ is symbolic form of "If $x$ has no courage, then $x$ will not win.
View full question & answer→MCQ 1171 Mark
Choose the conclusion of given statements:
All scientists working in America are talented. Some Indian scientists are working in America. Therefore, "Some Indian scientists are talented."
AnswerThe statement is true as it's already given that All scientists working in America are talented.
View full question & answer→MCQ 1181 Mark
Which of the following is a statement?
- A
- ✓
$11$ comes after $12$
- C
India is a beautiful country
- D
AnswerCorrect option: B. $11$ comes after $12$
“Close the door” is not a statement as it is an imperative sentence.
$“11$ comes after $12”$ is a statement as it is true.
“India is a beautiful country” is not a statement as opinion of beautifulness vary from person to person.
“This is useless” is not a statement as it involves this which doesn’t give any idea about what we are talking.
View full question & answer→MCQ 1191 Mark
$R$ the following statements.
$P:$ Suman is brilliant
$Q:$ Suman is rich
$R:$ Suman is honest
The negation of the statement “Suman is brilliant and dishonest if and only if Suman is rich” can be expressed as.
- ✓
$\sim (Q \rightarrow (P\ Λ \sim R))$
- B
$\sim Q \rightarrow ~P\ Λ\ R$
- C
$\sim P\ Λ\ \sim R) \rightarrow Q$
- D
$\sim P\ Λ\ (Q \rightarrow \sim R)$
AnswerCorrect option: A. $\sim (Q \rightarrow (P\ Λ \sim R))$
View full question & answer→MCQ 1201 Mark
Choose the correct answer:
The negation of the statement.
$“7$ is greater than $8”$ is.
AnswerCorrect option: B. $7$ is not greater than $8.$
Let $p: 7$ is greater than $8.$
$\sim p: 7$ is not greater than $8.$
View full question & answer→MCQ 1211 Mark
The negation of the statement $7$ is greater than $8$ is:
AnswerCorrect option: B. $7$ is not greater than $8.$
Statement: $7$ is greater than $8$
Negation: $7$ is not greater than $8$
View full question & answer→MCQ 1221 Mark
The converse of the statement $p \Rightarrow q$ is.
- A
$p \Rightarrow q$
- ✓
$q \Rightarrow p$
- C
$~p \Rightarrow q$
- D
$~q \Rightarrow p$
AnswerCorrect option: B. $q \Rightarrow p$
The converse of the statement $p \Rightarrow q$ is
$q \Rightarrow p$
View full question & answer→MCQ 1231 Mark
Choose the correct answer:
The negation of the statement.
“Plants take in $CO_2$ and give out $O_2$ ” is.
- A
Plants do not take in $CO_2$ and do not give out $O_2$
- ✓
Plants do not take in $CO_2$ or do not give out $O_2$.
- C
Plants take in $CO_2$ and do not give out $O_2$
- D
Plants take in $CO_2$ or do not give out $O_2$.
AnswerCorrect option: B. Plants do not take in $CO_2$ or do not give out $O_2$.
Let $p:$ Plants take in $CO_2$ and give out $O_2$
$q:$ Plants take in $CO_2$
$r:$ Plants give out $O_2$
$\sim q:$ Plants do not take in $CO_2$.
$\sim r:$ Plants do not give out$O_2$.
$\therefore\ \sim (q ^ r) = (\sim q \sim r):$ plants do not take in $CO_2$ or do not give out $O_2$
View full question & answer→MCQ 1241 Mark
The contra$-$positive of the statement If a triangle is not equilateral, it is not isosceles is:
- A
If a triangle is not equilateral, it is not isosceles
- B
If a triangle is equilateral, it is not isosceles
- C
If a triangle is not equilateral, it is isosceles
- ✓
If a triangle is equilateral, it is isosceles
AnswerCorrect option: D. If a triangle is equilateral, it is isosceles
Given, statement is:
If a triangle is not equilateral, it is not isosceles.
Now, contra$-$positive is:
If a triangle is equilateral, it is isosceles.
View full question & answer→MCQ 1251 Mark
Which of the following is true.
AnswerCorrect option: D. Everyone in India speaks Hindi.
The statement Everyone in India speaks Hindi is not true.
This is because, there are some states like Tamil nadu, Kerala, etc.
where the person does not speak Hindi.
View full question & answer→MCQ 1261 Mark
Earth is a planet. Choose the option that is a negation of this statement:
- A
- B
- C
Earth revolves round the sun
- ✓
AnswerNegation of statement $"P"$ is $"$not $P"$
View full question & answer→MCQ 1271 Mark
$f$ the Boolean expression $(p ⊕ q) ∧ (\sim p ⊗ q)$ is equivalent to $p ∧ q,$ where $⊕, eÎ\{∧, ∨\}$ then the ordered pair $(⊕, e)$ is $\sim .$
- A
$(∨, ∧)$
- B
$(∨, ∨)$
- ✓
$(∧, ∨)$
- D
$(∧, ∧)$
AnswerCorrect option: C. $(∧, ∨)$
View full question & answer→MCQ 1281 Mark
The inverse of the statement $"$If a number is divisible by $4$ then it is also divisible by $2"$ is:
- ✓
If a number is not divisible by $4,$ then it is not divisible by $2.$
- B
If a number is divisible by $4,$ then it is always divisible by $2.$
- C
If a number is not divisible by $4,$ then it is divisible by $2.$
- D
AnswerCorrect option: A. If a number is not divisible by $4,$ then it is not divisible by $2.$
a number is not divisible by $4$ is the negation of the hypothesis a number is divisible by $4$, and it is not divisible by $2$ is the negation of the conclusion it is also divisible by $2.$
View full question & answer→MCQ 1291 Mark
Which of the following is not negation of statement $“$Sum of $2$ and $3$ is greater than $4”\ ?$
- ✓
Sum of $2$ and $3$ is smaller than $4$
- B
Sum of $2$ and $3$ is smaller than or equal to $4$
- C
Sum of $2$ and $3$ is not greater than $4$
- D
It is false that sum of $2$ and $3$ is greater than $4$
AnswerCorrect option: A. Sum of $2$ and $3$ is smaller than $4$
Negation of greater is ‘not greater’. ‘Not greater’ means either smaller than or equal to.
So, “Sum of $2$ and $3$ is smaller than or equal to $4”, “$Sum of $2$ and $3$ is not greater than $4”, “$Sum of $2$ and $3$ is not greater than $4”$ are negation of the given statement.
And $“$Sum of $2$ and $3$ is smaller than $4”$ is not the negation of given statement as it should include equal to also.
View full question & answer→MCQ 1301 Mark
A sentence is called a mathematically accepted statement if
- A
- ✓
It’s either true or false but not both.
- C
- D
It’s neither true or false.
AnswerCorrect option: B. It’s either true or false but not both.
View full question & answer→MCQ 1311 Mark
Let $p, q, r$ denote arbitrary statements. Then the logically equivalent of the statement $p \Rightarrow (q ∨ r)$ is $\sim .$
- A
$(p ∨ q) \Rightarrow r$
- ✓
$(p \Rightarrow q)\ ∨\ (p \Rightarrow r)$
- C
$(p \Rightarrow ~q)\ ∧\ (p \Rightarrow r)$
- D
$(p \Rightarrow q) ∧ (p \Rightarrow ~r)$
AnswerCorrect option: B. $(p \Rightarrow q)\ ∨\ (p \Rightarrow r)$
View full question & answer→MCQ 1321 Mark
In the truth table for the statement $( \sim p \rightarrow \sim q) ∧ ( \sim q \rightarrow \sim p),$ the last column has the truth value in the following order is.
- A
$\text{TTTF}$
- B
$\text{FTTF}$
- C
$\text{TFFT}$
- ✓
$\text{TTTT}$
AnswerCorrect option: D. $\text{TTTT}$
View full question & answer→MCQ 1331 Mark
Which of the following is a preposition?
- A
- ✓
- C
A half open door is half closed
- D
View full question & answer→MCQ 1341 Mark
The connective in the statement “Earth revolves around the Sun and Moon is a satellite of earth" is:
AnswerGiven statement: Earth revolves around the Sun and Moon is a satellite of earth
Here, the connective word is “and.”
View full question & answer→MCQ 1351 Mark
Here are some words translated from an artificial language
mie pie is blue light
mie tie is blue berry
aie tie is rasp berry
Which words could possibly mean "light fly"?
AnswerIt is clear that pie means light.
So there can be only $2$ correct options, either pie zie or pie mie.
But mie means blue as it is common in the first two statements.
View full question & answer→MCQ 1361 Mark
Which of the following statements is false?
AnswerCorrect option: C. $81$ is a square and cube
Since Delhi and Mumbai both are cities in India so $“$Delhi and Mumbai are cities of India$”$ is true.
Since Chandigarh is the capital of both states Punjab and Haryana so $“$Chandigarh is capital of Punjab and Haryana$”$ is true.
Since $81$ is a square and not a cube so $“81$ is a square and cube$”$ is false.
Since $16$ is even number and is also divisible by $8$
so $“16$ is even number and divisible by $8”$ is true.
View full question & answer→MCQ 1371 Mark
The negation of $q\ ∨ \sim (p ∧ r)$ is.
- A
$\sim q\ ∨ (p ∨ r)$
- ✓
$\sim q\ ∧\ (p ∧ r)$
- C
$q\ ∨ (p ∨ r)$
- D
$\sim q ∧ (p ∨ r)$
AnswerCorrect option: B. $\sim q\ ∧\ (p ∧ r)$
View full question & answer→MCQ 1381 Mark
Which of the following statement is a conjunction.
- A
Ram and Shyam are friends
- B
Both Ram and Shyam are friends
- C
Both Ram and Shyam are enemies
- ✓
AnswerAll the statements are conjunction.
View full question & answer→MCQ 1391 Mark
Denial of a statement is called its:
AnswerIt is a fundamental concept that, denial of a mathematical statement is called its negation.
View full question & answer→MCQ 1401 Mark
A rectangle is a quadrilateral and its four sides are equal. Which is not correct?
- ✓
A rectangle is a quadrilateral is false.
- B
A rectangle has four sides is true.
- C
A rectangle is a quadrilateral is true.
- D
A rectangle has all sided equal is false.
AnswerCorrect option: A. A rectangle is a quadrilateral is false.
A rectangle has four sides so it is a quadrilateral.
All the four sides are not equal as two are equal and other two are equal.
View full question & answer→MCQ 1411 Mark
Which of the following is true?
- A
$p \Rightarrow q = \sim p \Rightarrow \sim q$
- ✓
$\sim (p \Rightarrow \sim q) = \sim p\ ∧ q$
- C
$\sim (\sim p \Rightarrow \sim q) = \sim p ∧ q$
- D
$\sim (\sim p \Rightarrow q) = [\sim (p \Rightarrow q) ∧ \sim (q \Rightarrow p)]$
AnswerCorrect option: B. $\sim (p \Rightarrow \sim q) = \sim p\ ∧ q$
View full question & answer→MCQ 1421 Mark
Choose the correct answer: Which of the following statement is a conjunction?
- A
Ram and Shyam are friends.
- B
Both Ram and Shyam are tall.
- C
Both Ram and Shyam are enemies.
- ✓
AnswerIf two simple statements $p$ and $q$ are connected by the word ‘and’, then the resulting compound statement $p$ and $q$ is called a conjunction of $p$ and $q.$
Here, none of the given statement is conjunction.
View full question & answer→MCQ 1431 Mark
Which of the following cannot be the negation of the statement “Delhi is in India”?
- A
- B
It is false that Delhi is in India.
- ✓
It is false that Delhi is not in India.
- D
It is not the case that Delhi is in India.
AnswerCorrect option: C. It is false that Delhi is not in India.
“Delhi is not in India”, “It is false that Delhi is in India”, “It is not the case that Delhi is in India” are negations of the given statement.
Negation of a statement can be formed by adding ‘it is false that’ or ‘it is not the case that’.
In statement “It is false that Delhi is not in India” two negation phrases are used which is wrong so it is not the negation statement.
View full question & answer→MCQ 1441 Mark
There are $25$ days in a month. This is.
View full question & answer→MCQ 1451 Mark
Which of the following proposition is a tautology?
- A
$\sim p\ ∧ (\sim p\ ∨ \sim q)$
- B
$\sim q ∧ (\sim p\ ∨ \sim q)$
- C
$(\sim p\ ∨ \sim q) ∧ (p\ ∨ \sim q)$
- ✓
$(\sim p\ ∨ \sim q) ∨ (p\ ∨ \sim q)$
AnswerCorrect option: D. $(\sim p\ ∨ \sim q) ∨ (p\ ∨ \sim q)$
View full question & answer→MCQ 1461 Mark
The symbolic form of a statement "It is not true that Kiran passed therfore he is said' is.
AnswerCorrect option: B. $(p \rightarrow q)$
View full question & answer→MCQ 1471 Mark
Which one of the following is a tautology?
AnswerCorrect option: A. $(p ∧ (p \rightarrow q)) \rightarrow q$
View full question & answer→MCQ 1481 Mark
Which of the following is not a statement?
AnswerCorrect option: D. $x + 3 = 10, \text{x ÎR.}$
View full question & answer→MCQ 1491 Mark
Which statement is logically equivalent to "If Yoda cannot use a lightsaber then he cannot help Luke win the battle":
- A
Yoda cannot use a lightsaber and he will help Luke win the battle.
- ✓
If Yoda can help Luke win the battle then he can use a lightsaber.
- C
Yoda can use a lightsaber if and only if he can help Luke win the battle.
- D
Yoda cannot use a lightsaber and will not help Luke win the battle.
AnswerCorrect option: B. If Yoda can help Luke win the battle then he can use a lightsaber.
A statement is logically equivalent to its contrapositive To form the contrapositive switch the "If" and "then" sections of the statement $\text{AND}$ insert $\text{"NOTs"}$ into each section Notice in this situation that inserting $\text{"NOTs"}$ turns the thoughts positive $($you are negating negative thoughts$).$
View full question & answer→MCQ 1501 Mark
If $p$ and $q$ are mathematical statements, then in order to show that the statement $“p$ and $q”$ is true, we need to show that:
- A
The statement $p$ is true and the statement $q$ ement $p$ is true and the statement $q$ is not true.
- B
The statement $p$ is false and the statement $q$ is true.
- C
The statement $p$ is true and the statement $q$ is false.
- ✓
The statement $p$ is true and the statement $q$ is true.
AnswerCorrect option: D. The statement $p$ is true and the statement $q$ is true.
View full question & answer→