Question

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

Answer 1

Let q and r be statements.
Here,
q: If x is an integer and x² is odd.
r: x is also odd.
Then, p is" if q, then r".
Let r be false.
So, x is not an odd integer, i.e., x is an even integer.
Let: \[x = 2n\]  for some integer n

or, 

\[x^2 = 4 n^2\] 

In other words, x² is an even integer.
Now, q is false.
Thus, r is false; this implies q is false.
Hence, p is a true statement.