For the following claim Below you must disprove it. "For all integers x, x^2 + 1 is odd" Use the oddx = 2k+1 rule as well

for part b of the question, how did we get 2 answers after isolating for x?

This is a practice question from my Discrete Mathematical Structures Course. Thank you.

Please use the following definitions of even and odd numbers: • An integer a is even if there exists an integer z with a = 2z. An integer a is odd if there exists an integer z with a = 2z + 1. Your proofs may use the fact that every integer is either even or odd, but not both. Using Cases in a Proof Show that if a, b are real numbers then: |a| + |6| > |a + b|