Propsitions (what ever they are)?

Question

A friend asked me this question as i am the local math whiz but my forte is in the calculus area and i have no idea what this stuff even means;

Q = (p implys not q) or r

P = (p implys q) implys r

p = true

q = false

r = unknown

Prove that P = Q

Any help?

Answer 1

Q: "p implies q" is true if p is false or q true, in this case "not q" is true, so "true or r" is true.

P: "p implies q" is false because p is true but q is false, so we get "false implies r" which is true.

P=Q because both are true