MATHS (Each question 2 marks)

The component statements are as follows. p: Number 3 is prime. q: Number 3 is odd. Both the statements are true.

Statement p can be written as follows. If a positive integer is prime, then it has no divisors other than 1 and itself. The converse of the statement is as follows. If a positive integer has no divisors other than 1 and itself, then it is prime. The contra positive of the statement is as follows. If positive integer has divisors other than 1 and itself, then it is not prime.

The component statements are as follows. p: All integers are positive. q: All integers are negative. Both the statements are false.

The compound statement with ‘And’ is “25 is a multiple of 5 and 8”. This is a false statement, since 25 is not a multiple of 8. The compound statement with ‘Or’ is “25 is a multiple of 5 or 8”. This is a true statement, since 25 is not a multiple of 8 but it is a multiple of 5.

The contra positive is as follows. If you know how to reason deductively, then you can comprehend geometry. The converse is as follows. If you do not know how to reason deductively, then you cannot comprehend geometry.

1. This is the contra positive of the given statement.
2. This is the converse of the given statement.

The contra positive is as follows. If something does not have low temperature, then it is not cold. The converse is as follows. If something is at low temperature, then it is cold.

Here, the connecting word is ‘or’. The component statements are as follows. p: Square of an integer is positive. q: Square of an integer is negative.

The given statement can be written in five different ways as follows.

1. A triangle is equiangular implies that it is an obtuse-angled triangle.
2. A triangle is equiangular only if it is an obtuse-angled triangle.
3. For a triangle to be equiangular, it is necessary that the triangle is an obtuse-angled triangle.
4. For a triangle to be an obtuse-angled triangle, it is sufficient that the triangle is equiangular.
5. If a triangle is not an obtuse-angled triangle, then the triangle is not equiangular.

Here, the connecting word is ‘and’. The component statements are as follows. p: All rational numbers are real. q: All real numbers are not complex.

The component statements are as follows. p: 100 is divisible by 3. q: 100 is divisible by 11. r: 100 is divisible by 5. Here, the statements, p and q, are false and statement r is true.

The given statement can be written as follows. If it is a sunny day, then I go to a beach. The converse of the statement is as follows. If I go to a beach, then it is a sunny day. The contra positive of the statement is as follows. If I do not go to a beach, then it is not a sunny day.

Here, the connecting word is ‘and’. The component statements are as follows. p: The sand heats up quickly in the sun. q: The sand does not cool down fast at night.

The contra positive is as follows. If a number x is not odd, then x is not a prime number. The converse is as follows. If a number x is odd, then it is a prime number.

1. This is the contra positive of the given statement.
2. This is the converse of the given statement.

The given statement can be written as follows. If x is an even number, then x is divisible by 4. The contra positive is as follows. If x is not divisible by 4, then x is not an even number. The converse is as follows. If x is divisible by 4, then x is an even number.

The converse of statement r is as follows. If you feel thirsty, then it is hot outside. The contra positive of statement r is as follows. If you do not feel thirsty, then it is not hot outside.

The contra positive is as follows. If two lines intersect in the same plane, then they are not parallel. The converse is as follows. If two lines do not intersect in the same plane, then they are parallel.