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Logic ChAPTER 3

Logic ChAPTER 3. Variations of the Conditional and Implications 3.4. Variations of the conditional. Variations of p → q. Converse: Inverse: Contrapositive:. p → q is logically equivalent to ~ q → ~ p q → p is logically equivalent to ~ p → ~ q. Examples of variations.

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Logic ChAPTER 3

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  1. LogicChAPTER 3

  2. Variations of the Conditional and Implications3.4

  3. Variations of the conditional Variations of p→q Converse: Inverse: Contrapositive: p→q is logically equivalent to ~q→~p q→p is logically equivalent to ~p→~q

  4. Examples of variations p: n is not an even number. q: n is not divisible by 2. Conditional: p→q If n is not an even number, then n is not divisible by 2. Converse:q→p If n is not divisible by 2, then n is not an even number. Inverse:~p→~q If n is an even number, then n is divisible by 2. Contrapositive:~q→~p If n is divisible by 2, then n is an even number.

  5. Equivalent Equivalent

  6. Conditional Equivalents

  7. Biconditional Equivalents

  8. Examples of variations • Given: h: honk • u: you love Ultimate • Write the following in symbolic form. Honk if you love Ultimate. If you love Ultimate, honk. Honk only if you love Ultimate. A necessary condition for loving Ultimate is to honk. A sufficient condition for loving Ultimate is to honk • To love Ultimate, it is sufficient and necessary that you honk. or

  9. A statement that is always true is called a tautology. A statement that is always false is called a contradiction. Tautologies and Contradictions

  10. Example Show by means of a truth table that the statement p↔~p is a contradiction.

  11. Implications The statement p is said to imply the statement q,p q, if and only if the conditional p→q is a tautology.

  12. Example Show that END

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