Show that the following statement is true by the method of the contrapositive p : “If x is an integer and x 2 is odd, then x is also odd.”

Question

Philoid · Accepted Answer

Let us Assume that q and r be the statements given

q: x is an integer and x² is odd.

r: x is an odd integer.

since the given statement can be written as :

p: if q, then r.

Let r be false . then,

x is not an odd integer, then

x is an even integer

x = (2n) for some integer n

x² = 4n²

x² is an even integer

Thus, q is False

Therefore, r is false q is false

Hence, p: “ if q, then r” is a true statement.