Given below are some pairs of statements. Combine each pair using if and only if : (i)p : If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. q : If a number is divisible by 3, then the sum of its digits is divisible by 3.

Home » Given below are some pairs of statements. Combine each pair using if and only if : (i)p : If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. q : If a number is divisible by 3, then the sum of its digits is divisible by 3.

Given below are some pairs of statements. Combine each pair using if and only if :
(i)p : If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. q : If a number is divisible by 3, then the sum of its digits is divisible by 3.

RS Agarwal Maths Class 11 Mathematical Reasoning

Given below are some pairs of statements. Combine each pair using if and only if :
(i)p : If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. q : If a number is divisible by 3, then the sum of its digits is divisible by 3.

A number is divisible by 3 if and only if the sum of the digits of the number is divisible by 3.

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By giving a counter-example, show that the following statement is false : p : If all the sides of a triangle are equal, then the triangle is obtuse angled.

Use contradiction method to prove that :

By giving a counter-example, show that the statement is false :
p : If n is an odd positive integer, then n is prime.

Consider the statement :
q : For any real numbers a and b, a2 = b2⇒ a = b
By giving a counter-example, prove that q is false.

Let p : If x is an integer and x2 is even, then x is even, Using the method of contrapositive, prove that p is true.

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By giving a counter-example, show that the following statement is false : p : If all the sides of a triangle are equal, then the triangle is obtuse angled.

Use contradiction method to prove that :

By giving a counter-example, show that the statement is false :
p : If n is an odd positive integer, then n is prime.

Consider the statement :
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By giving a counter-example, prove that q is false.

Let p : If x is an integer and x2 is even, then x is even, Using the method of contrapositive, prove that p is true.

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