Use truth tables to determine whether or not the arguments a

Use truth tables to determine whether or not the arguments are valid...  (you don\'t have to write out each truth tables if you don\'t want to, but could you at least setup the expressions that you will use in the truth tables like (P v Q), (R v S) therefore (P v R)

A) Jane and Pete won\'t both win the math prize.Pete will win either the math prize or the chemistry prize. Jane will win the math prize. Therefore, Pete will win the chemistry prize.

B) The main course will be either beef or fish. The vegetable will be either peas or corn. We will not have both fish as a main course and corn as a vegetable. Therefore, we will not have both beef as a main course and peas as a vegetable.

C) Either John or Bill is telling the truth. Either Sam or Bill is lying. Either Sam or Bill is lying. Therefore, either John is telling the truth or Sam is lying.

D) Either Sales will go up and the boss will be happy or expenses will go up and the boss won\'t be happy. Therefore, sales and expenses will not both go up.

Solution

I will submit answer.