Show that the following statement is true by the method of contrapositive
p: If x is an integer and x² is even, then x is also even

Solution:

Let us assume that the given statement to be p and its components be q and r. i.e.,

p: If x is an integer and x² is even, then x is also even.

Let q : x is an integer and x² is even.

r : x is even.

To prove that p is true by the contrapositive method, we will prove "if not r then not q". So we assume that r is false. i.e., x is not even.

"x is not even" implies that "x² is also not even".

Therefore, q is false. Thus, the given statement p is true by the method of contrapositive

NCERT Solutions Class 11 Maths Chapter 14 Exercise 14.5 Question 3

Show that the following statement is true by the method of contrapositive. p: If x is an integer and x² is even, then x is also even

Summary:

The given statement is proved to be true by the method of contrapositive