(9 marks) Let p and q be statements, and consider the following six statements.
p ∧ ∼ q
p ∨ q
∼ p ∧ q
p → q
q → p
∼ q

(a) Determine the maximum number of these six statements that can be simultaneously true,
and which truth values for p and q are needed to obtain this maximum. Explain your
reasoning.
(b) Use ∧ or ∨ to combine two of these six statements to give a contradiction, and use the laws
of logical equivalence to prove that your statement is a contradiction.
(c) Use ∧ or ∨ to combine two of these six statements to give a tautology, and use the laws of
logical equivalence to prove that your statement is a tautology.