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Lesson 20 INTERPRETING TRUTH TABLES. Review Conditional Statements (Less. 17) Original If p, then q. Converse If q, then p. Inverse If ~p, then ~q. Contrapositive.

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Presentation on theme: "Lesson 20 INTERPRETING TRUTH TABLES. Review Conditional Statements (Less. 17) Original If p, then q. Converse If q, then p. Inverse If ~p, then ~q. Contrapositive."— Presentation transcript:

1 Lesson 20 INTERPRETING TRUTH TABLES

2 Review Conditional Statements (Less. 17) Original If p, then q. Converse If q, then p. Inverse If ~p, then ~q. Contrapositive If ~q, then ~p. What is special about the original conditional statement and its contrapositive? They are logically equivalent statements We will discover this is also true for the converse and inverse statements

3 Biconditional Statement A biconditional statement is a combination of the original conditional statement and its converse using “… if and only if …” Original conditional statement If p, then q. Biconditional Statement p if and only if q. A biconditional statement is true only when both the original and converse are true If an animal is a bird, then it has two legs. a.Write the converse & find its truth value If an animal has two legs, then it is a bird. False, kangaroo b.Write as a biconditional & find its truth value. Why? An animal is a bird if and only if it has two legs. False, converse is false

4 Truth Table A truth table is a table that lists all possible combinations of truth values for a hypothesis, conclusion, and the conditional statement(s) they form  Copy for homework and tests  You will be asked to add columns Take note of the only combination that is false Why is a conditional statement true even when both the hypothesis & conclusion is false? You can conclude anything from a false conclusion (same for the previous line) HypothesisConclusionIf p, then q. TTT TFF FTT FFT

5 If a polygon is a quadrilateral, then the figure has four sides. a.Use a truth table to represent the statement. b.Add to the truth table to show the converse and biconditional. pqIf p, then q. If q, then p. p if and only if q.

6 If a polygon is a quadrilateral, then the figure has four sides. a.Use a truth table to represent the statement. We know this is a true statement, but row #1 in the truth table shows why. b.Add to the truth table to show the converse and biconditional. pqIf p, then q. If q, then p. p if and only if q. TTT TFF FTT FFT

7 If a polygon is a quadrilateral, then the figure has four sides. a.Use a truth table to represent the statement. We know this is a true statement, but row #1 in the truth table shows why. b.Add to the truth table to show the converse and biconditional. pqIf p, then q. If q, then p. p if and only if q. TTTT TFFT FTTF FFTT

8 If a polygon is a quadrilateral, then the figure has four sides. a.Use a truth table to represent the statement. We know this is a true statement, but row #1 in the truth table shows why. b.Add to the truth table to show the converse and biconditional. If a polygon has four sides, then the figure is a quadrilateral. A polygon is a quadrilateral if and only if it has four sides. pqIf p, then q. If q, then p. p if and only if q. TTTTT TFFTF FTTFF FFTTT

9 Compound statement combines 2 statements using and/or. CONJUNCTION Uses “and” To be true both p and q must be true p – salt has sodium q – salt has chloride Salt has sodium and chloride. True DISJUNCTION Uses “or” To be true at least one of p and q must be true p – the light is on q – the room is dark The light is on or the room is dark. True

10 Conclusion/Questions? Is a true biconditional statement a conjunction or disjunction? Why? Conjunction because a biconditional requires a true p and a true q. Why do you think disjunction is true in more cases than a conjunction? A disjunction only requires that one of the two statements is true, while a conjunction requires that both be true. pqp and qp or q TTTT TFFT FTFT FFFF


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