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Exploring Truth Tables: Connectives, Conditionals, and Logical Equivalence

This segment delves into truth tables, emphasizing additional connectives that enhance compound statements. It explains conditionals (if-then statements), how they connect hypotheses with conclusions, and their truth values. The biconditional is presented as a connection defined by "if and only if," being true only when both statements share the same truth values. Equivalent statements are defined as those yielding identical truth values. Tautologies and self-contradictions are also discussed, showcasing always-true and always-false statements, respectively. Join us as we explore these intriguing concepts in logical reasoning.

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Exploring Truth Tables: Connectives, Conditionals, and Logical Equivalence

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Presentation Transcript

  1. Truth Tables, part 2

  2. New stuff… • Truth tables can have additional connectives to form even better compound statements.

  3. Conditional • A conditional is an if-then statement that connects a hypothesis (if) with a conclusion (then). It is only false when it has a true hypothesis and a false conclusion. Its truth table will look like this:

  4. Conditional • A conditional is an if-then statement that connects a hypothesis (if) with a conclusion (then). It is only false when it has a true hypothesis and a false conclusion. Its truth table will look like this:

  5. Biconditional • A biconditional is two statements being connected by “if an only if”. Since it is both the conditional and its converse, it is true when both statements have the same truth values. Its truth table will look like this:

  6. Biconditional • A biconditional is two statements being connected by “if an only if”. Since it is both the conditional and its converse, it is true when both statements have the same truth values. Its truth table will look like this:

  7. Equivalent Statements • Statements that yield the same truth values (in the last column) are considered logically equivalent. These statements are different ways of saying the same thing.

  8. Equivalent Statements • Statements that yield the same truth values (in the last column) are considered logically equivalent. These statements are different ways of saying the same thing.

  9. Tautology • A tautology is a compound statement that is always true. In a tautology, all the truth values in the final column will be true.

  10. Tautology

  11. Self-Contradictions • A self-contradiction is a compound statement that is always false. In a self-contradiction, all the truth values in the final column will be false.

  12. Now you try a few… • 1) • 2)

  13. You knew it was going to happen... • p. 124; #10-12, 16-18 even, 26-30 even • (it will keep you out of trouble while your parents are at Open House, tonight from 5:45 to 8:45!)

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