GENERAL MATHEMATICS 11
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1 HE SEED MONESSORI SCHOOL GENERAL MAHEMAICS 11 ruth Values and ruth ables July 19, 2016
2 WORK PLAN Daily Routine Objectives Starter Lesson Proper Practice Exercises Exit Card
3 OBJECIVES At the end of the period, you are expected to be able to: determine truth values of propositions; and construct truth tables
4 SARER ell whether the statement is true or false is an even number. 2. If the sum of two angles is 180, then they are supplementary. 3. All dogs are animals and all animals are dogs. 4. If you multiply two numbers, then the product is either positive or negative. 5. If you see lightning and you hear thunder, then it is raining somewhere near, and if it is raining somewhere near, then you see lightning and you hear thunder.
5 SARER ell whether the statement is true or false is an even number. ALSE 2. If the sum of two angles is 180, then they are supplementary. RUE 3. All dogs are animals and all animals are dogs. ALSE 4. If you multiply two numbers, then the product is either positive or negative. ALSE 5. If you see lightning and you hear thunder, then it is raining somewhere near, and if it is raining somewhere near, then you see lightning and you hear thunder. RUE
6 EXPLORAION A teacher promised her student, If you pass the final examination and you submit all the requirements, then you may join the graduation. he student only passes the final examination; however, the teacher allows her to join the graduation. Did the teacher break her promise?
7 DEINIION he truth value of a proposition is either RUE () or ALSE (), but not both. In computer science and programming, 1 represents RUE and 0 represents ALSE.
8 DEINIION A truth table is used to summarize all the possible combinations of truth values of a given proposition.
9 LESSON PROPER 1. Negation. he negation is true if and only if the truth value of the proposition is false. P ~P P: 1 is an even number. () ~P: 1 is not an even number. ()
10 LESSON PROPER 2. Disjunction. he disjunction is true if and only if at least one of the disjuncts is true. P Q P v Q
11 EXAMPLES P Q P v Q P: I will clean the bathroom. Q: I will clean the kitchen. P v Q: I will clean either the bathroom or the kitchen. Analysis: I lied only if I did not clean the bathroom or I did not clean the kitchen. hat is, v.
12 LESSON PROPER 3. Conjunction. he conjunction is true if and only if both conjuncts are true. P Q P ^ Q
13 EXAMPLES P Q P ^ Q P: I will clean the bathroom. Q: I will clean the kitchen. P ^ Q: I will clean both the bathroom and the kitchen. Analysis: I lied if I did not clean even just one of the two choices.
14 LESSON PROPER 4. Implication. he implication is true in all cases EXCEP when the consequent is false when the antecedent is true. P Q P Q
15 EXAMPLES P Q P Q P: I will clean the bathroom. Q: I will clean the kitchen. P Q: If I will clean the bathroom, then I will clean the kitchen. Analysis: I lied only if I did not clean the kitchen after I cleaned the bathroom.
16 EXAMPLES 1. Construct a truth table for: ~( P ^ Q ). P Q P ^ Q ~(P^Q)
17 EXAMPLES 2. Construct a truth table for: P v (Q ~P) P Q ~P Q ~P P v (Q ~P)
18 LOOKING BACK A teacher promised her student, If you pass the final examination and you submit all the requirements, then you may join the graduation. he student only passes the final examination; however, the teacher allows her to join the graduation. Did the teacher break her promise?
19 LOOKING BACK irst, symbolize the statement. If you pass the final examination and you submit all the requirements, then you may join the graduation. Let: P = he student passes the finals. Q = he student submits all the requirements. R = he student may join the graduation. ( P ^ Q ) R
20 LOOKING BACK P Q R Next, construct the truth table for (P^Q) R. ( P ^ Q ) R P ^ Q
21 LOOKING BACK P Q R But which one is his case? ( P ^ Q ) R P ^ Q P = ; Q = ; R =
22 LOOKING BACK Write the conclusion. Since the result is true, it means that the teacher did not break her promise.
23 LOOKING BACK But what if the teacher did not allow him to join the graduation, did she break her promise?
24 LOOKING BACK P Q R Which one is this case? ( P ^ Q ) R P ^ Q P = ; Q = ; R =
25 LOOKING BACK he result is still true. Meaning, the teacher s decision not to allow him to join the graduation is still acceptable.
26 EXERCISES Pair Work: On your notebook, copy and answer numbers 1-10 of irm Up, page 212.
27 EXERCISES Answers:
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