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P: You vote in the election. Q: You are a registered voter. R: You are a minor. 1. If you vote in the election then you are a registered voter. 2. If you are not a minor and you are a registered voter then you vote in the election

P: You vote in the election. Q: You are a registered voter. R: You are a minor. 1. If you vote in the election then you are a registered voter. 2. If you are not a minor and you are a registered voter then you vote in the election

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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WRITE THE FOLLOWING IN SYMBOLIC FORM OR IN STATEMENTS FORM USING P, Q & R FOR STATEMENTS AND ~, ^. V, , , FOR SYMBOLS. P: You vote in the election. Q: You are a registered voter. R: You are a minor. 1. If you vote in the election then you are a registered voter. 2. If you are not a minor and you are a registered voter then you vote in the election. 3. ~ Q ( R ^ ~ P ) 4. P v ~ R Q
•Disjunction {either, unless} •Conditional {If, implies, provided that, in case, whenever, } •Biconditional {when and only when, is necessary and sufficient for} Logical Connectives • Let P, Q, and R or any variable be a proposition. Q P^Q PvQ T T F F T F F F F F F Write the following in symbolic form using p, q, and r for statements and symbols {~, ^, v, →, +→}. •p: Pres. Duterte is a good President •q: Government officials are corrupt •r: People are happy a. If Pres. Duterte is a good President, then the government officials are not corrupt. Answer: p →~q b. If Pres. Durterte is not a good President and people are not happy, then government officials are corrupt. Answer: (~p^~ r) → q Write the following in symbolic form using p, q, and r for statements and symbols {~, ^, v, →, +→}. •p: Pres. Duterte is a good President •q: Government officials are corrupt •r: People are happy c. Pres. Duterte is a good President, if and only if the government officials are not corrupt. Answer: p → ~q
Transcribed Image Text:•Disjunction {either, unless} •Conditional {If, implies, provided that, in case, whenever, } •Biconditional {when and only when, is necessary and sufficient for} Logical Connectives • Let P, Q, and R or any variable be a proposition. Q P^Q PvQ T T F F T F F F F F F Write the following in symbolic form using p, q, and r for statements and symbols {~, ^, v, →, +→}. •p: Pres. Duterte is a good President •q: Government officials are corrupt •r: People are happy a. If Pres. Duterte is a good President, then the government officials are not corrupt. Answer: p →~q b. If Pres. Durterte is not a good President and people are not happy, then government officials are corrupt. Answer: (~p^~ r) → q Write the following in symbolic form using p, q, and r for statements and symbols {~, ^, v, →, +→}. •p: Pres. Duterte is a good President •q: Government officials are corrupt •r: People are happy c. Pres. Duterte is a good President, if and only if the government officials are not corrupt. Answer: p → ~q
The following is its truth table F F Today is Tuesday. Today is not Tuesday. Today is a sunny day. Today is not a sunny day. Exercises: • What is the negation of the following statement? a. P: V2 is a rational number. b. Q: 7 is an odd number. c. R: Makati is the capital of the Philippines. • Solution: a. P: V2 is not a rational number. b. Q: 7 is not an odd number. c. R: Makati is not the capital of the Philippines. Logical Connectives • It is a symbol used to connect two or more proposition or predicate logics. Five(5) Common Logical Connectives • Conjunction • Disjunction and(^) or(v) • Conditional " Biconditional • Negation "only if" / "if...then( → ) "if only if" ( →) "not" ( –/~) The following are some phrases: •Conjunction {but, yet, while, whereas, still, despite, although, however, because, since, until}
Transcribed Image Text:The following is its truth table F F Today is Tuesday. Today is not Tuesday. Today is a sunny day. Today is not a sunny day. Exercises: • What is the negation of the following statement? a. P: V2 is a rational number. b. Q: 7 is an odd number. c. R: Makati is the capital of the Philippines. • Solution: a. P: V2 is not a rational number. b. Q: 7 is not an odd number. c. R: Makati is not the capital of the Philippines. Logical Connectives • It is a symbol used to connect two or more proposition or predicate logics. Five(5) Common Logical Connectives • Conjunction • Disjunction and(^) or(v) • Conditional " Biconditional • Negation "only if" / "if...then( → ) "if only if" ( →) "not" ( –/~) The following are some phrases: •Conjunction {but, yet, while, whereas, still, despite, although, however, because, since, until}
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