Question

The contrapositive of the converse of the statement, “If x is a prime number then x is odd” is
a) If x is not a prime number then x is odd.
b) If x is not an odd number then x is not a prime number.
c) If x is a prime number then it is not odd.
d) If x is not a prime number then x is not an odd.

Answer 1

Hint: Contrapositive simply means inversing the statement like – Ram is taller than Golu. Its contrapositive will be that Golu is not taller than Ram. Also, converse of conditional statements means interchanging the hypothesis and the conclusion – like Golu is taller than Shyam, then Shyam is taller than Ram.

Complete step-by-step answer:
It is given in the question to find the contrapositive and converse of the statement “If x is a prime number then x is odd”. To find the contrapositive and converse of the given statement then we have to look at basic contrapositive and converse.
Contrapositive means simply inverting the given statement The contrapositive of a conditional statement of the form "If P then Q" is "If ~Q then ~P". Symbolically, the contrapositive of P Q is ~Q ~P. For example “x is an even number then x is a natural number”. Its contrapositive statement will be “If x is not a natural number then x is not even number” This is just an example. And converse means interchanging the conclusion i.e the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q → P, For example the converse of the above statement given by interchanging the two statements “If x is a natural number then x is an even number”.

On the basis of the above discussion we will now find the contrapositive and converse of the given statement in the question “If x is a prime number then x is odd”. Converse statement will be – If x is odd then x is prime number and again Contrapositive of the above statement will be “If x is not a prime number, then x is not an odd number”.This is the required answer

Option ‘d’ is the right answer.

Note: Generally students misunderstood converse as if it is the statement with opposite meaning but opposite meaning but actually it is just the interchanged statement having some conclusion. Like – ‘x’ is a prime number then x is odd, here - we will write as “if x is odd then x is prime number”.