3. Show that the following statement is true by the method of contrapositive.
p: If x is an integer and is even, then is also even.
Given, If x is an integer and is even, then is also even.
Let, p : x is an integer and is even
q: is even
In order to prove the statement “if p then q”
Contrapositive Method: By assuming that q is false, prove that p must be false.
q is false: x is not even x is odd x = 2n+1 (n is a natural number)
Hence is odd is not even
Hence p is false.
Hence the given statement is true.
Create Your Account