Answer
(a) The election is not decided.
(b) The election is not decided, and the votes have been counted.
(c) The votes have not been counted.
(d) If the votes have been counted then the election is decided.
(e) If the votes have not been counted then the election is not decided.
(f) If the election is not decided then the votes have been counted.
(g) If and only if the election is decided will the votes have been counted.
(h) Either the votes have not been counted, or the election is not decided and the votes have been counted.
Work Step by Step
p="the election is decided," and q="the votes have been counted." In this problem, we simply substitute the phrases for the variables in the compound propositions
(a) not p
(b) not p and q
(c) not q
(d) if q then p
(e) if not q then not p
(f) if not p then not q
(g) if and only if p then q
(h) not q or (not p and q)
