Can someone help me with these questions? I need an answer to all of it, please. Could you explain it to me? ASAP? 7. Let ∈ ℕ. Prove that “if x is even, then is even” using the following proof techniques:
a) Direct proof
b) Induction

8. Prove or disprove: For , ∈ ℤ, if | and |, then = .

9. Recall the definition of prime numbers and divisibility. Prove For all primes p and integers a and b, if | then | or |.