Logic Worksheet With Answers Page 8
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22b. q (~p ~r):
“A student studies, and if the student does not miss class,
then the student does not fail.”
If a symbolic statement appears without parentheses, statements before and after the most
dominant connective should be grouped.
The dominance of connectives used in symbolic logic is defined in the following order:
Most dominant:
Biconditional
Same level of dominance:
Conjunction
Disjunction
Conditional
Least dominant:
Negation
~
Statement
Most Dominant
Statements Meaning Clarified
Type of
Connective Highlighted
with Grouping Symbols
Statement
in Red
Conditional
p
q
~r
p
q
~r
p
(q
~r)
Conditional
p
q
~r
p
q
~r
(p
q)
~r
Biconditional
p
q
r
p
q
r
p
(q
r)
Biconditional
p
q
r
p
q
r
(p
q)
r
Conditional
p
~q
r
s
p
~q
r
s
(p
~q)
(r
s)
The meaning is ambiguous.
?
p
q
r
p
q
r
Ex: Let p, q, and r represent the following simple statements.
p: I fail the course.
q: I study hard.
r: I pass the final.
~p (q r )
a. “I do not fail the course if and only if I study hard and I pass the final”
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