LECTURE 4: MORE LOGIC (
§
2.52.8)
All truths are easy to understand once they are discovered; the point is to discover them.
Galileo
Galilei (1564  1642)
1.
More terminology for implications
Let
P
and
Q
be statements. Recall that
P
⇒
Q
has the following truth table:
P
Q
P
⇒
Q
T
T
T
T
F
F
F
T
T
F
F
T
We can read this in many ways: “If
P
(is true) then
Q
(is true).” “
P
implies
Q
.” “
Q
if
P
.” “
P
only
if
Q
.” “
P
is sufficient for
Q
.” “
Q
is sufficient for
P
.”
We call
P
the
premise
and
Q
the
conclusion
of the implication
P
⇒
Q
.
What if we switch the premise and conclusion and form the new statement
Q
⇒
P
? Is this the same
thing?
No! Try the following example: “If it rains on me then I get wet.” This is true, but if we switch the
premise and conclusion we get “If I get wet then it rains on me.” which is false.
When we switch the premise and conclusion, and form
Q
⇒
P
we call this the
converse
of
P
⇒
Q
.
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 Spring '11
 Smith
 Logic, Galileo Galilei, compound statements

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