NCERT Class XI Mathematics - Mathematical Reasoning - Solutions

Question : 16

Total: 25

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:

The given compound statement is of the form “if p then q”
p: x ∈ Z and x2 is even.
q: x is an even integer.
We assume that q is false, then x is not an even integer.
⇒ x is an odd integer. ⇒ x2 is an odd integer. ⇒ p is false
So, when q is false, p is false.
Thus, the given compound statement is true.

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