March 09, Logic 2.notebook 25) D 26) D 27) C

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1 25) D 26) D 27) C 17) If you eat Nano yogurt then you live to an old age 18) If you care about your family then you take pictures with a Blinko camera 19) If you get good gas mileage then you drive a Suberb car 20) If you make a better chicken dinner then you use Dust & Roast 21) If you don't send Trademark cards then you don't care enough to send the very best 22) If you have body odor then you don't use Trickle deodorant 23) If your teeth aren't pearly white then you don't brush with Brite 24) If you don't get a HS diploma then you won't get a good job 1

2 28) If today is Friday, then tomorrow is Saturday. Converse : If tomorrow is then today is Friday Inverse : If today is not Friday, then tomorrow is not Saturday. Contrapositive : If tomorrow is not Saturday then today is not Friday. 29) If Douglas does well in college, then he will apply to medical school. Converse : If Douglas applies to medical school then he does well in college. Inverse : If Douglas doesn't do well in college, then he will not apply to medical school. Contrapositive : If Douglas doesn't apply to medical school then he doesn't do well in college 30) Arlette will get a role in the play if she auditions. 30) If Arlette auditions then she will get a role in the play. Converse : If Arlette gets a role in the play then she auditioned. Inverse : If Arlette doesn't audition then she didn't get a role in the play Contrapositive : If Arlette doesn't get a role in the play then she didn't audition 31) Dorothea will graduate from law school in January if she takes courses this summer. 31) If Dorothea takes courses this summer then she will graduate from law school in January Converse : If Dorothea graduates from law school in January then she took courses in the summer Inverse : If Dorothea doesn't take courses in the summer, then she won't graduate from law school in January Contrapositive : If Dorothea doesn't graduates from law school in January then she didn't take courses in the summer 32) If John is accepted at the Culinary Institute, then he has a chance of earning a high salary as a chef. Converse : If John has a chance of earning a high salary as a chef then he was accepted at the Culinary Institute. Inverse :If John is not accepted at the Culinary Institute, then he doesn't have a chance of earning a high salary as a chef. Contrapositive : If John doesn't have a chance of earning a high salary as a chef then he wasn't accepted at the Culinary Institute. 33) If a man is honest, he does not steal. Converse : If a man does not steal then he is honest. Inverse : If a man is not honest then he does steal Contrapositive : If a man does steal then he is not honest. 34) If Julia doesn t water the plants, then the plants will die. Converse : If the plants die then Julia doesn t water the plants Inverse : If Julia does water the plants, then the plants will not die. Contrapositive : If the plants don't die, then Julia waters the plants 35) Rachel will not get her allowance if she forgets to do her chores. If Rachel forgets to do her chores, then she will not get her allowance Converse : If Rachel doesn't get her allowance then she forgot to do her chores. Inverse : If Rachel doesn't forget to do her chores, then she will get her allowance. Contrapositive : If Rachel does get her allowance then she didn't forget to do her chores. 2

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4 Do Now : 1) Give an example of an open statement 2) What is the measure of an angle that is supplementary to 106 o? 4

5 A conditional statement and it's contrapositive are LOGICALLY EQUIVALENT This question is asked by using the sentences or the symbols 1)What statement is logically equivalent to : "If I eat cereal then I am hungry " 2)What statement is logically equivalent to : "It will snow if the temperature is 20 o " 3)What statement is logically equivalent to : "If the meal has chicken in it, Melanie will not eat it" 4)What statement is logically equivalent to : "I will go for a walk if it is not dark out." 5

6 Conditional Inverse Converse Contrapositive Which columns are logically equivalent? 6

7 Just a reminder : When writing an if...then statement from a hidden conditional the word "when" is a substitute for "if" Quick pracce : Express the hidden conditional in a sentence using if...then When the cafeteria is full students like to go to the library. 7

8 We are going to be learning a few laws in logic Each of the laws are VALID ARGUMENTS We are going to use these laws to draw conclusions that are TRUE 8

9 The law of Detachment p p q q premise conclusion I am given a conditional statement that is TRUE I am given the hypothesis and that is TRUE You conclude that the conclusion is TRUE Think about the conditional chart and when a conditional is TRUE p q p q 9