For the following statements the universe comprises all nonzero integers. Determine the truth value of each statement.
a) ∃x ∃y [xy =1]
b) ∃x ∀y [xy = 1]
c) ∀x ∃y [xy = 1]
d) ∃x ∃y [(2x + y = 5) ˄ (x – 3y = –8)]
e) ∃x ∃y [(3x – y = 7) ˄ (2x + 4y = 3)]
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