Logic Worksheet With Answers Page 6
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22Ex: Let p and q represent the following simple statements:
p: It is freezing.
q: It is cold.
The statement “If it is freezing then it is cold” can be written as “p
q”.
The statement “If it is not cold then it is not freezing” can be written as “~q
~p”.
Common English expressions for p q:
Symbolic Statement
English Statement
Example:
p: It is freezing.
q: It is cold.
p q
If p then q
If it is freezing then it is cold.
p q
q if p
It is cold if it is freezing.
p q
p is sufficient for q
Being freezing is sufficient to
be cold.
p q
q is necessary for p
Being cold is necessary for
being freezing.
p q
p only if q
It is freezing only if it is cold.
p q
Only if q, p
Only if it is cold is freezing.
Biconditional statements are conditional statements that are true if the statement is still true
when the antecedent and consequent are reversed.
The compound statement “p if and only if q” (abbreviated as iff ) is symbolized by p q.
Common English Expressions for p q:
Symbolic Statement
English Statement
Example:
th
p: It is 4
of July;
q: It is the Independence Day.
p q
th
p if and only if q
It is 4
of July if and only if it is
the Independence Day.
p q
q if and only if p
It is the Independence Day if
th
and only if it is 4
of July.
p q
th
If p then q, and if q then p.
If is 4
of July then is the
Independence Day, and if is the
th
Independence Day then is 4
of
July.
p q
th
p is necessary and sufficient
Being 4
of July is necessary
for q
and sufficient for being the
Independence Day.
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