1 Marks Question

Question 2011 Mark

Identify the Quantifiers in the following statement:
There exists a triangle which is not equilateral.

Answer

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
There exists.

Question 2021 Mark

State the converse and contrapositive of the following statements:
I go to a beach whenever it is a sunny day.

Answer

Converse:
If I go to a beach, then it is a sunny day.
Contrapositive:
If I do not go to a beach, then it is not a sunny day.

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Question 2031 Mark

State the converse and contrapositive of the following statements:
If a quadrilateral is a parallelogram, then its diagonals bisect each other.

Answer

Converse:
If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Contrapositive:
If the diagonals of a quadrilateral do not bisect each other, then it is not a parallelogram.

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Question 2041 Mark

Write the negation of the following statements:
There exists $\text{x}\in\text{N},\text{x}+3=10$

Answer

The Negation of the statement:
There exists $\text{x}\in\text{N},\text{x}+3=10$
is
For every $\text{x}\in\text{N},\text{x}+3\not=10$

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Question 2051 Mark

Translate the following statement into symbolic form:
x and y are even integers.

Answer

p: x is even integers.q: y is even integers.
p ∧ q: x andy are even integers.

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Question 2061 Mark

Write down the contrapositive of the following statement:
If x = y and y = 3, then x = 3.

Answer

If x ≠ 3, then x ≠ y or y ≠ 3.

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Question 2071 Mark

Write down the negation of following compound statement:
A triangle has either 3-sides or 4-sides.

Answer

Let p: A triangle has 3-sides.
q: A triangle has 4-sides.
Then, the negation of the given compound statement is:
~(p v q): A triangle has neither 3-sides nor 4-sides.

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Question 2081 Mark

Write down the negation of following compound statement:
$x = 2$ and $x = 3$ are roots of the Quadratic equation $x^2 - 5x + 6 = 0.$

Answer

Let $p; x = 2$ is root of quadratic equation $x^2 - 5x + 6 = 0.$
$q: x = 3$ is root of quadratic equation $x^2 - 5x + 6 = 0.$
Then, the negation of the given compound statement is:
$\sim(p ∧ q): x = 2$ is not a root of quadratic equation $x^2- 5x + 6 = 0$ or $x = 3$ is not a root of the quadratic equation $x^2 – 5x + 6 = 0.$

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Question 2091 Mark

Write the component statements of the following compound statements and check whether the compound statement is true or false:
Square of an integer is positive or negative.

Answer

The component statements of the given compound statement are:

Square of an integer is positive.
Square of an integer is negative.

The compound statement is true because the first statement is true. Since the connective used is "or" and one of the component statements is true, the compound statement is true.

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Question 2101 Mark

State the converse and contrapositive of the following statements:
A positive integer is prime only if it has no divisors other than 1 and itself.

Answer

Converse:
If a positive integer has no divisors other than 1 and itself, then it is prime.
Contrapositive:
If a positive integer has some divisors other than 1 and itself, then it is not prime.

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Question 2111 Mark

Which of the following sentences are statements? Justify.Every set is an infinite set.

Answer

We know that is either true or false but not both simultaneously.
It is false. Hence, it is a statement.

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Question 2121 Mark

Identify the Quantifiers in the following statement:
There exists a real number which is not a rational number.

Answer

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
There exists.

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Question 2131 Mark

Find out the following sentences are statements and which are not. Justify your answer.
The product of (-1) and 8 is 8.

Answer

It is an assertive sentence; therefore, it is a statement. But -1 × 8 = -8 therefore, the statement is false.

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Question 2141 Mark

Determine the contrapositive of the following statements:
If he has courage he will win.

Answer

If he does not win, then he does not have courage.

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Question 2151 Mark

Find the component statements of the following compound statements.
$\sqrt{7}$ is a rational number or an irrational number.

Answer

p: $\sqrt{7}$ is a rational number.
q: $\sqrt{7}$ is a irrational number.

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Question 2161 Mark

Find out the following sentences are statements and which are not. Justify your answer.
All real numbers are complex numbers.

Answer

It is true because we can write a real number as x + 0 i. So, it is a true statement.

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Question 2171 Mark

Find out the following sentences are statements and which are not. Justify your answer.
Go!

Answer

It is an exclamatory sentence, so it is not a statement.

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Question 2181 Mark

Identify the Quantifiers in the following statement:
For all negative integers $x, x^3$ is also a negative integers.

Answer

Quantifier are the phrases like ‘There exists’ and ‘For every1, ‘For all’ etc.
For all.

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Question 2191 Mark

Form the biconditional statement p ↔ q, where.
p: The unit digit of an integer is zero.
q: It is divisible by 5.

Answer

p ⟷ q: The unit digit of on integer is zero, if and only if it is divisible by 5.

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Question 2201 Mark

Find out the following sentences are statements and which are not. Justify your answer.
Every set is a finite set.

Answer

It is a false assertive sentence because there are some sets that are infinite like the set of all real numbers. Therefore, it is a statement.

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MATHS 1 Marks Question