Aim: Conditional, Converse & Inverse Course: Math Lit. Aim: What is a conditional statement? Its converse? Its inverse? Do Now: Construct a truth table.

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Aim: Conditional, Converse & Inverse Course: Math Lit. Aim: What is a conditional statement? Its converse? Its inverse? Do Now: Construct a truth table for the following compound statement: Alfie did not come last night and did not pick up his money. p represents ‘Alfie did come last night.’ q represents ‘Alfie picked up his money.’ pq T T F F T F T F T F F T F F T T F F T F ~p ~q ~p ˄ ~q The only time the compound statement is true is when both p and q are false.

Aim: Conditional, Converse & Inverse Course: Math Lit. Conditional Statement A conditional is a compound sentence formed by combining two simple sentences with the connective words “if..., then...” The “if” part of the conditional is called the antecedent, hypothesis or premise. The “then” part is called the conclusion or consequent. If the glove fits, then you must acquit! antecedent,hyp othesis, premise conclusion, consequent “if.. then” indicates a logical relationship – the consequent follows logically from the antecedent.

Aim: Conditional, Converse & Inverse Course: Math Lit. 1.If you send in the proof of purchase, then they will send you a get well card. 2.If Mr. Mazes assigns homework, you’d better do it. Rewrite each in if-then form and underline as above. Identify the hypothesis and conclusion in the following by underlining the hypo once and the conclusion twice: 1. “Vote for me and I’ll whip unemployment.” 2.For good health, exercise regularly. Hidden conditionals “If you vote for me, then I’ll whip unemployment.” “If you exercise regularly, then you will have good health.”

Aim: Conditional, Converse & Inverse Course: Math Lit. If New Mexico is a state containing the word New, then New Mexico borders an ocean. If 9 is an odd number, then 9 is a prime number. Conditional and Truth Values Is this conditional statement true? If the name of a state contains the word New, then the state borders an ocean. To show that a conditional is false, you need to find only one example for which the hypothesis is true and the conclusion is false New Mexico F F9 is not prime -

Aim: Conditional, Converse & Inverse Course: Math Lit. Find an example for each statement that shows it to be false. 1.If it is not a weekday, then it is Saturday. 2.If you live in a country that borders the United States, then you live in Canada. 3.If your last name is Vladimir, then you must be Russian. Sunday Mexico SI Yankee Vladimir Hernandez is a Black Hispanic ball player

Aim: Conditional, Converse & Inverse Course: Math Lit. Conditional - Symbolically antecedent if.. p consequent then.. q  What’s the truth? “If I receive my check tomorrow, then I will pay you the $10 I owe you.” Let p rep I receive my check tomorrow Let q rep I will pay you the $10 I owe you. pq p  q TT TF FT FF T F T T Conditional Truth Table

Aim: Conditional, Converse & Inverse Course: Math Lit. Model Problems r: It is Tuesday j: I am in school Write symbolically: 1)If it is Tuesday, then I am in school 2)If it is not Tuesday, then I am not in school. p: I am hungry q: I want a sandwich Write sentence for 1)p  q2) q  p 3) ~p  q4) ~q  p r  j ~r  ~j 1) If I am hungry, then I want a sandwich. 2) If I want a sandwich, then I am hungry. 3) If I am not hungry, then I don’t want a sandwich. 4) If I don’t want a sandwich, then I am not hungry.

Aim: Conditional, Converse & Inverse Course: Math Lit. Translations for Conditional The if part of a conditional need not be stated first. Conditional translation Example If p, then q.If you are 18, then you can vote. q, if p.You can vote, if you are 18. p, only if qYou are 18 only if you can vote. all p are qAll 18-year-olds can vote. hidden conditionals

Aim: Conditional, Converse & Inverse Course: Math Lit. Model Problems Construct a truth table for the following statement. (p ˄ q)  p pq T T F F T F T F F T F F T T T T p ˄ q (p ˄ q)  p

Aim: Conditional, Converse & Inverse Course: Math Lit. Model Problems If you do not itemize deductions on Schedule A and you have charitable contributions then complete the worksheet on page 14 and enter the allowable part on line 34b. Understand the problem Devise a plan Carry out the plan Look back d: You itemize deductions in Sched A. c: You have charitable contributions. w: You complete the worksheet on page 14. b: You enter the allowable part on line 34b. If not d and c, then (w and b). (~d ˄ c)  (w ˄ b) Interpret the sentence. rephrase and represent symbolically

Aim: Conditional, Converse & Inverse Course: Math Lit. Model Problems If you do not itemize deductions on Schedule A and you have charitable contributions then complete the worksheet on page 14 and enter the allowable part on line 34b. If not d and c, then (w and b). (~d ˄ c)  (w ˄ b) Is statement true if d, c, w, and b are all true? (~T ˄ T)  (T ˄ T) (F ˄ T)  (T ˄ T) F  T T

Aim: Conditional, Converse & Inverse Course: Math Lit. Converse and Inverse If a polygon is a quadrilateral, then it has four sides. If a polygon has four sides, then it is a quadrilateral. If a polygon is not a quadrilateral, then it does not have four sides. Describe what happened to this conditional in each of the following: Hypothesis and Conclusion switched places Both Hypothesis and Conclusion were negated Converse Inverse

Aim: Conditional, Converse & Inverse Course: Math Lit. For the sentence that follows a.Write a conditional & determine its truth value. b.Write its converse and inverse A right angle has a measure of a. If an angle is a right angle, then it’s measure is T b.Converse - If an angle’s measure is 90 0, then the angle is a right angle. c. Inverse - If an angle is not a right angle, then it’s measure is not 90 0.

Aim: Conditional, Converse & Inverse Course: Math Lit. Write the converse and inverse for the following conditional and determine the truth value of all three sentences. If a figure is a square, then it is a rectangle. T Converse - If a figure is a rectangle, then it is a square. F Inverse - If a figure is a not square, then it is not a rectangle. T

Aim: Conditional, Converse & Inverse Course: Math Lit. Summary of Conditionals StatementForm Conditional Converse Inverse If, then If not, then not Conditional – If an angle is a straight angle, then its measure is Converse – If an angle’s measure is 180 0, then it is a straight angle. Inverse– If an angle is not a straight angle, then its measure is not hypothesis- conclusion

Aim: Conditional, Converse & Inverse Course: Math Lit. Truth Table pq~p~q pqpq ~p  ~qq  p converse inverse T T F F T F T F F F T T T T T F F F T T T F T T T F T T conditional

Aim: Conditional, Converse & Inverse Course: Math Lit. Assume the following statement is true: p  ~q If you obey the law, then you will not go to jail. Model Problem Write the converse and inverse and tell which are true. converse: ~q  p If you do not go to jail, then you obey the law. F inverse: ~p  q If you do not obey the law, then you will go to jail. F p q