MATHS 1 Marks Question

The argument used to check the validity of the given statement is not correct because it does not produce a contradiction.

True. Because, for any two integers, if x - y is positive then -(x - y) is negative.

Negation of the given statement:

It is not true that it rained on July 4, 2005.

Or

It did not rain on July 4, 2005.

The statement is:
r: 60 ism ultiple of 3 or 5
is a com pound statement of the following statements:
p: 60 is multiple of 3
q: 60 is multiple of 5
Suppose q is false. That is, 60 is not a multiple of 5. Clearly p is true.
Thus, if we assume that q is false, then p is true.
Hence, the statement is true i.e. the statement "r" is a valid statement.

Negation of the given statement:

It is not true that Bangalore is the capital of Karnataka.

Or

Bangalore is not the capital of Karnataka.

It is necessary to have a passport to log on to the server.

The component statements of the given compound statement are:

1. x = 2 is the root or the equation 3x² - x - 10 = 0.
2. x = 3 is the root or the equation 3x² - x - 10 = 0.

The connective used is "and". So, both component statements must be true for the compound statement to be true. The statement "x = 3x = 3 is the root or the equation 3x² - x - 10 = 0" is false. Therefore, the compound statement is false.

Inclusive OR because a person could have both ration card as well as passport.

If it rains, then it is cold.

Converse:
If you have winter clothes, then you live in Delhi.
Contrapositive:
​If you do not have winter clothes, then you do not live in Delhi.

The component statements of the given compound statement are:

1. To enter into a public library, children need an identity card from the school.
2. To enter into a public library, children need a letter from the school authorities.

The compound statement is true because both component statements are true.

The component statements of the given compound statement are:

1. Square of an integer is positive.
2. 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.

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.

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

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.

If Max does not study, then he will not pass the test.

Negation of the given statement:

The sun is not cold.

Or

It is not true that the sun is cold.

You watch television if and only if your mind is free.

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.

False. Because, a chord does not have to pass through the centre.

Let q and r be the statements given by
q: lf x is an integer and x² is odd
r: x is an odd integer.
Then, p: " lf q, thenr."
If possible, let r be false. Then,
r is false
⇒ x is not an odd integer
⇒ x is an even integer
⇒ x = (2n) for some integer n
⇒ x² = 4n²
⇒ x² is an even integer
⇒ q is false.
Thus, r is false ⇒ q is false.
Hence, p: "if q, then r" is a true statement.

The statement is:
"125 is multiple of 5 and 7"
Since 125 is a multiple of 5 but it is not a multiple of 7. So, q is not a true statement i.e. the statement "q" is not a valid statement.

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.

Negation of the given statement:
Some students did not complete their homework.

Mathematics could be easy for some people, so this sentence may or may not be true. So, it is not a statement.

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

The given statement in this pair are the negation of each other.

It is a false assertive sentence, so it is a false statement.

It is a false assertive sentence. Two non-empty sets with no common elements can have an empty intersection. Therefore, it is a statement.

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

Exclusive OR is used because students can opt for either Hindi or Sanskrit as their third language.

You get an A grade if and only if you do all the homework regularly.

Without knowing the sentence, we cannot decide whether it is true or false. So, it is not a statement.

It is not true that every rhombus is a square because some rhombi may have all angles other than 90. So, it is a false statement.

True. Because a circle is an ellipse that has equal axes.

We cannot decide whether this sentence is true or false without knowing the value of x. So, it is not a statement.

If she does not earn money, then she will not work.

If it rains, then there is a traffic jam.

Inclusive OR is used because a person can have both passport as well as voter registration card.

If he tires, then he will not win.

A quadrilateral is a rectangle if and only if it is equiangular.

Negation of the given statement:
There exists a number which is not equal to its square.