Use proof by contradiction to prove that if for an integer a, `a^2` is even, then so is a.

Use proof by contradiction to prove that if for an integer a, a^2 is divisible by 3, then a is divisible by 3.

Use proof by contradiction to show that there is no value of n for which 6n ends with the digit zero.

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

Prove that the sum of two odd numbers is even.

Let r be a rational number and x be an irrational number. Use proof by contradiction to show that r+x is an irrational number.

Prove by contradiction that two distinct lines in a plane cannot intersect in more than one point.

Prove that 2^(n) gt n for all positive integers n.

If a and b are distinct integers, prove that a-b is a factor of a^n - b^n , whenever n is a positive integer.

Verify by the method of contradiction that sqrt(2) is irrational .