Logic Worksheet With Answers Page 15
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22Ex: Write the equivalent contrapositive for the statement “If you live in Houston, then you live in
Texas”.
p: You live in Houston.
q: You live in Texas.
p q.
If you live in Houston, then you live in Texas:
~q ~p,
The contrapositive is in symbolic form:
so that we can write it as an English statement: “If you do not live in Texas, then you do not live
in Houston”.
Variations of the Conditional Statement
Name
Symbolic Form
English Translation
Conditional
If p, then q.
p q
Converse
If q, then p.
q p
Inverse
If not p, then not q.
~p ~q
~
Contrapositive
If not q, then not p.
~p
Practice Ex: Show that only the contrapositive is logical equivalent with the conditional p q.
Practice Ex: Show that Converse and Inverse are equivalent.
Ex: The statement “If it’s freezing then is cold” can be written p q,
where
p: It’s freezing
q: It’s cold.
Converse:
p is “If it’s cold then is freezing”
Inverse:
~p ~q is “If it’s not freezing then is not cold”
Contrapositive: ~
~p is “If it’s not cold then is not freezing”
Part 6: Negations of Conditional Statements and De Morgan’s Laws
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