Show that the following statement is true by the method of the contrap

1.	Show that the following statement is true by the method of the contrapositive p : “If x is an integer and x2 is odd, then x is also odd.”
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 x²is an even integer Thus, q is False Therefore, r is false ⇒ q is false Hence, p: “ if q, then r” is a true statement.

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

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

x²is an even integer

Thus, q is False

Therefore, r is false ⇒ q is false

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