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1. (10 points) Please complete the following truth table.
A B C A ∧ C ¬B ¬(A ⇒ C) ((¬A) ∨ B)) ∧ C (B ⇒ (A ∨ C)) ⇔ ((C ∨ (∼ B)) ⇒ A)
T F T
F T T
c
2. (10 points) Let A,B,C ⊂ U for some universe U. Please show that C −(A∪B) is a subset of A −B.
3. (5 points) Suppose that A and B are statements. Is B =⇒ A the same as A ∨¬B? Please explain why or why not.