The question ask:
Use proof by contrapositive to show that if a positive integer is the product of two distinct primes, then its square root is irrational.
So I have not(q) -> not(p) as follows:
If the square root of a positive integer is rational then it is not the product of two distinct primes.
One issue I have is I think I have already found a counter example that goes against this.
Lets say the positive integer was 36.
The Square root of 36 is 6, which is rational.
The prime factorization for 36 would be. 2 * 2 * 3 * 3.
Which would mean it has 2 distinct primes of 2 and 3.
Did I go somewhere wrong with my setup of the contrapositive or my understanding of what 2 distinct primes means?
Thanks in advance.