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CONDITIONAL – TRUTH TABLE

CONDITIONAL – TRUTH TABLE. Unlike other truth tables, the truth table for a conditional can be a bit confusing!. Let’s look at the following example: If you clean your room, then you can go to the movies. This proposition has the standard form if p, then q where

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CONDITIONAL – TRUTH TABLE

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  1. CONDITIONAL – TRUTH TABLE

  2. Unlike other truth tables, the truth table for a conditional can be a bit confusing!

  3. Let’s look at the following example: If you clean your room, then you can go to the movies. This proposition has the standard form if p, then q where p = you clean your room and q = you can go to the movies Let’s consider each of the four possible cases for the truth value of if p, then q.

  4. Determining whether the conditional statement is true depends on if its components are true. If you cleaned your room (T) and got to go to the movies (T), then the conditional is true (T). If you cleaned your room (T) and did not get to go to the movies (F) then the conditional is false (F). If you didn't clean your room (F) and got to go to the movies (T), then the conditional is true (T). If you didn't clean your room (F) and did not get to go to the movies (F) then the conditional is true (T).

  5. These last two probably seem strange. Think of it this way: if your father made the original statement to you, under what conditions was he lying? The only time we know for sure he lied was if you cleaned your room and he wouldn't let you go. If you didn't clean your room, we don't know what he would have done so we have to assume he was telling the truth.

  6. The Truth Table for Conditional if p, then q p q p  q T T T T F F F T T F F T Conditional Let p and q be propositions. The proposition if p, then q (p  q), is the proposition that is true in all cases except when the antecedent is true and the conclusion is false.

  7. Truth Tables for Converse, Inverse, and Contrapositive CONDITIONAL CONVERSE INVERSE CONTRAPOSITIVE If p, then q p  q If q, then p q  p If p, then q p q If q, then p qp p q p q

  8. Truth Tables for Converse, Inverse, and Contrapositive CONDITIONAL CONVERSE INVERSE CONTRAPOSITIVE If p, then q p  q If q, then p q  p If p, then q p q If q, then p qp p q p q TTFF TFTF FFTT FTFT TFTT TTFT TTFT TFTT

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