Logic Worksheet With Answers Page 7
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22p q
q is necessary and sufficient
Being the Independence Day is
for p
necessary and sufficient for
th
being 4
of July.
Ex: Let p and q represent the following simple statements:
p: She is laughing.
q: She is happy.
~(p
q):
“It is not true that she is laughing and is happy”;
~p
q:
“She is not laughing and she is happy”;
~(p
q):
“She is neither laughing nor happy” or “”It is not true that she is laughing or is
happy”
Expressing Symbolic Statements with Parentheses in English
Symbolic Statement
Statements to Group Together
English Translation
If q and not p, then not r.
(q
~p)
~r
q
~p
q, and if not p then not r.
q
( ~p
~r)
~p
~r
Remark: When we translate the symbolic statement into English, the simple statements in
parentheses appear on the same side of the comma.
Ex: Let p, q, and r represent the following simple statements:
p: A student misses class.
q: A student studies.
r: A student fails.
a. (q ~ p) ~ r:
“If a student studies and does not miss class, then the student does
not fail.”
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