For each of the following:
a. Play with the statement - i.e., Look at/test a few examples. (See if there are any counter-examples.)
b. If the statement is true, roof of the statement. Else, provide a counter-example showing th the statement is false (state how your example satises the hypothesis but fails to meet the conclusion).
In all statements, m, n, a, and b are assumed to be integers unless otherwise stated.
Statement 1. If m is an even integer, then 5m^2 + 7m is an even integer.
Statement 2. If n is an odd integer, then n^2 + n + 41 is an odd integer.
Statement 3. If n is a positive integer, then n^2 + n + 41 is a prime number.
Statement 4. If m and n are odd integers, then mn + 2 is an odd integer.
Statement 5. If m and n are odd primes, then mn + 2 is a prime number.
Statement 6. If a and b are odd integers, then a^2 + b^2 is an even number.
Statement 7. If a^2 + b^2 is an even number, then a and b are odd integers.