EECS 203-1: Discrete Mathematics Winter 2005 Introductory ...

The conditional connective
• One connective that gets a big workout in logic is the conditional p → q.
It is read “if p then q”, ”p is sufficient for q, ”a necessary condition for p is
q”, “p only if q”, and ”q whenever p”.
• You can think of this as a “one-way biconditional”. The truth table is
p q p → q
T T T
T F F
F T T
F F T
• One way to read this table is that ”q is at least as true as p is, and maybe
more,” as in the third line. Another way to read it is ”p can’t be true and q
false.” This has some strange repercussions. For example,
is true (by line 4). Equally,
is true.
if 2 + 2 = 5, then Kevin Bacon is the Pope
if 2 + 2 = 5, then Kevin Bacon is not the Pope
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