Inverses, converses, and contrapositives - Logic
Inverses, converses, and contrapositives
Lessons
Notes:
Let be the hypothesis and 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:
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A converse statement is formed by switching the hypothesis and the conclusion of the conditional. In symbolic form it would be:
A contrapositive statement is formed by negating both the hypothesis and conclusion, AND switching them. In symbolic form it would be:
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Statements which always have the same truth values are logical equivalents.
Conditionals and contrapositives are logical equivalents, and inverses and converses are logical equivalents.
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Intro Lesson
The inverse, converse, and contrapositive Overview:
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1.
Finding the inverse, converse and contrapositive
Given the statements, write the inverse, converse, and contrapositive: -
2.
For each statement, write the inverse, converse, and contrapositive in symbolic form:
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3.
Truth value of inverse, converse and contrapositive
Write the converse, and find the truth value of the converse: -
4.
Assume that the conditional statement is true. Write the inverse and state whether the inverse is always true, sometimes true, or never true:
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5.
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?
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6.
Finding truth values of original statements
Find possible truth values for and where:
