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 contrapositivep: “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. 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 and 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 contrapositivep: “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.

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 and q is false

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