Question

Consider the following statement: The square of a prime number is not prime. (a) Write this as an if-then statement, using careful mathematical language and notation. (b) Prove or disprove the statement.

Answer 1

The square of a prime number is not prime.

a) let x ∈ R, If x ∈ {prime numbers}, then
`x^(2)`∉{prime numbers}

there says that if x is a real and x is in the set of the prime numbers, then the square of x isn't in the set of prime numbers.

b) Prove or disprove the statement.

ok, if x is a prime number, then x only can be divided by himself. Now is easy to see that
`x^(2)` = x*x can be divided by himself and x, then x*x is not a prime number, because can be divided by another number different than himself