3.5_djj_004_Notes.notebook. November 03, 2009
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1 IN CLASS TUE, ,THU, , & TUE Section 3.5: Equivalent Statements, Variations of Conditional Statements, and De Morgan's Laws (Objectives 1 5) Equivalent Statements: statements that have the same truth values in every possible case, symbolized. Construct a truth table for ~q ~p. Recall: They have the same "answer column". Therefore: p q ~q ~p Oct 11 12:31 PM 1
2 Oct 27 10:41 AM 2
3 Use this equivalent pattern to write a statement equivalent to this conditional: If you live in Tallahassee, then you live in Florida. "You live in Florida, if you live in Tallahassee." "You live in Tallahassee only if you live in Florida." "If you do not live in Florida, then you do not live in Tallahassee." contrapositive. Write the converse, inverse, and contrapositive of the following: "If it rains, then it pours." Converse: If it pours, then it rains. (NOT L.E. to p >q) Inverse: If it does not rain, then it does not pour. (NOT L.E. to p >q) Contrapositive: If it does not pour, then it does not rain. Oct 11 12:35 PM 3
4 Write the converse, inverse, and contrapositive of the following: p ~ q Converse: Inverse: Contrapositive: Write the converse, inverse, and contrapositive of the following: "If the cable is out, then we cannot watch TV." Converse: Inverse: Contrapositive: Oct 11 12:39 PM 4
5 Are these variations equivalent to the conditional? Hw.#2a: Use a truth table to show that p q and ~p q are equivalent. Oct 11 12:41 PM 5
6 ========We got to here on TUE =========== Write 2 statements that are equivalent to: "If the shoe fits, then wear it." Either the shoe doesn't fit, or I will wear it. If I don't wear the shoe, then it does not fit. Oct 11 12:44 PM 6
7 LAW OF THE DOUBLE NEGATIVE ~ ~ p p Oct 29 9:32 AM 7
8 Write the negation of: "If I'm late, then I'll apologize." I am late and I won't apologize. Write the negation of: "If the shoe fits, then wear it." The shoe fits and I don't wear it. Oct 11 12:45 PM 8
9 BEGIN HERE TUE If you clean up your room, then you can go to Europe. Rephrase: Negate: Oct 29 9:41 AM 9
10 De Morgan s Laws Construct a truth table for ~(p q). Construct a truth table for ~p ~q. They have the same "answer column". Therefore: ~(p q) ~p ~q This is one of De Morgan's laws for logic! Oct 11 12:48 PM 10
11 Nov 3 10:23 AM 11
12 Use this equivalent pattern to write a statement equivalent to: It is not true that (Florida and Georgia are both islands). Recall from Section 3.2: p: Jon is at work. q: Mary is at home. ~( p q ): It is not true that Jon is at work and Mary is at home. ~p ~q: Jon is not at work and Mary is not at home. Are they equivalent statements? According to one of De Morgan's laws, what is ~( p q ) equivalent to? Oct 11 12:52 PM 12
13 What might De Morgan's other law state is equivalent to ~ (p q)? Oct 11 12:54 PM 13
14 Use De Morgan's laws to negate and. Negate: This house is too small or we have too many children. Negate: The car is old and it is not reliable. Negate: All movies are enjoyable and some movies are dramas. Oct 11 2:55 PM 14
15 Use De Morgan's laws to write a statement that is equivalent to this statement: "It is not true that I am wrong and you are right." Use De Morgan's laws to write a statement that is equivalent to this statement: "It is not the case that the movie is interesting or entertaining." Note: The double negation of a statement is equivalent to the statement. Therefore, ~ (~ p) p. Use this and De Morgan s law to derive the disjunction equivalent to the conditional. ~ [~ (p q)] ~[p ~q] ~p q) Oct 11 2:56 PM 15
16 It can be tedious to use truth tables to determine whether or not statements are equivalent. Hw. #18: Select the statement that is not equivalent to: " It is not true that England and Africa are both countries." a. If England is a country, then Africa is not a country. b. England is not a country and Africa is not a country. c. England is not a country or Africa is not a country. d. If Africa is a country, then England is not a country. We'll focus on those that can be done using pattern recognition. Determine which of the statements is equivalent to: 'If the bills are paid, then I can sleep." a. If the bills are not paid, then I cannot sleep. b. The bills are not paid or I can sleep. c. If I can sleep, then the bills are paid. d. The bills are paid and I cannot sleep. See text ex Use packet pages on Negations and Equivalent Statements. Oct 11 3:00 PM 16
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