6) (2.5 points] Use a table to express the values of the Boolean function: F(x, y, z) = xy + (xyz) 0 0 ola 0 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 1 1 1 4) [3 points] Using contraposition, prove that if 3n+4 is even, then n is even, where n is an integer. 5) [4 points) Prove the bi-conditional: n is odd = 5n + 2 is odd, where n is integer. a) Alice is a mathematics major. Therefore, Alice is either a mathematics major or a computer science major. b) Jerry is a mathematics major and a computer science major. Therefore, Jerry is a mathematics major. c) If it is rainy, then the pool will be closed. It is rainy. Therefore, the pool is closed. d) If it snows today, the university will close. The university is not closed today. Therefore, it did not snow today. e) If I go swimming, then I will stay in the sun too long. If I stay in the sun too long, then I will sunburn. Therefore, if I go swimming, then I will sunburn. 2) [3 points] Use rules of inference to show that if Vx(P(x) VQ(x)) and Vx((-P(x) ^ Q(x)) = R(x)) are true, then Vx-R(x) P(x)) is also true, where the domains of all quantifiers are the same