The (Ultimate) Geometry Review Sheet Page 4
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15Biconditionals (…if and only if…)
6.
Symbol:
Truth Table:
p q
p
q
T
T
T
T
F
F
F
T
F
F
F
T
7.
Tautology
Compound sentence that is always true (T)
8.
Logically Equivalent Statements
Two statements that always have the same truth values
De Morgan’s Law
9.
Premise:
~(p q)
~p ~q
Conclusion:
Premise:
~(p q)
~p ~q
Conclusion:
10.
Conditional, Converse, Inverse, Contrapositive
Conditional:
p q
Converse:
q p
Inverse:
~p ~q
Contrapositive:
~q ~p
Conditionals and Contrapositives are logically equivalent: (p q) (~q ~p)
11.
Law of Contrapositives
Premise:
p q
~q ~p
Conclusion:
12.
Law of Modus Ponens (Law of
Detachment)
p q
Premise:
Premise:
p
q
Conclusion:
13.
Law of Modus Tollens
Premise:
p q
Premise:
~q
~p
Conclusion:
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