Inverses, converses, and contrapositives - Logic

Inverses, converses, and contrapositives

Lessons

Notes:

Let pp be the hypothesis and qq 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:

~pp \to ~qq

A converse statement is formed by switching the hypothesis and the conclusion of the conditional. In symbolic form it would be:

q pq\ \to p

A contrapositive statement is formed by negating both the hypothesis and conclusion, AND switching them. In symbolic form it would be:

~qq \to ~pp

Statements which always have the same truth values are logical equivalents.
Conditionals and contrapositives are logical equivalents, and inverses and converses are logical equivalents.

  • Intro Lesson
    The inverse, converse, and contrapositive Overview:
  • 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:
  • 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:
  • 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?

  • 6.
    Finding truth values of original statements

    Find possible truth values for pp and qq where:

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Inverses, converses, and contrapositives

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