GNED 1101 Chapter Notes - Chapter 1.5: Contraposition

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1.5 Equivalent Statements and Variations of Conditional Staements
Equivalent Compound Statements
Are made up of the simple statements and have the same corresponding truth values
for all true-false combinations of these simple statements
o If a compound statement is true then its equivalent statement must also be true
(and vice versa)
Example; show that pq is equivalent to p→q
P Q
q
pq
p
p→q
T T
F
T
F
T
T F
T
T
F
T
F T
F
F
T
F
F F
T
T
T
T
The table shows that the truth values for both statements is the same
The symbol is used to show that two statements are equivalent
o (p) is a double negation.
The negation cancels out and the statement becomes p
Thus (p)p
o Thus, The double negation of a statement is equivalent to the statement
Variations of the Conditional Staetment
The contrapositive of a conditional statement is a statement obtained by reversing and
negating the antecedent and the consequent
Example;
o P Q is the statements symbolic form
o Q P is the contrapositive. Revrse the statements and negate them
The Converse is when the antecedent and consequent are reversed but not negated
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