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Conjunctions and disjunctions
Inverses, converses, and contrapositives
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Let ppp be the hypothesis and qqq be the conclusion. Then:
An inverse statement is formed by negating both the hypothesis and conclusion of the conditional. In symbolic form it would be:
~ppp →\to→ ~qqq
A converse statement is formed by switching the hypothesis and the conclusion of the conditional. In symbolic form it would be:
q →pq\ \to pq →p
A contrapositive statement is formed by negating both the hypothesis and conclusion, AND switching them. In symbolic form it would be:
~qqq →\to→ ~ppp
Statements which always have the same truth values are logical equivalents.
Conditionals and contrapositives are logical equivalents, and inverses and converses are logical equivalents.
Find the truth value of the following conditionals. Then write the contrapositive and find the truth value of the contrapositive. Are the truth values the same?
Find possible truth values for ppp and qqq where:
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