Use predicate logic to state the following sentences. Be sure to define all predicates, constants, and variables.

a. Not all birds can fly.

b. Every child is younger than its mother.

c. Mary and Sue have the same paternal grandfather.

Prove that p (q r) = (p q) (p r)

a. using a truth table.

b. using natural deduction (show the rules that you apply at each step of the proof).