EXERCISESDIRECTIONS: Answer the following questions below and put your answer in the space provider.Formalize the given statements using the following propositions.p: Paul is happy.q: Queenie is happy.r: Paul plays guitar.1. Both Paul and Queenie are happy.2. Paul plays the guitar provided that he is happy.3. IF Paul is happy and plays the guitar, then Queenie is not happy.Let M: Mark is English and L: Lem is German. Translate the following logic symbols intowords.4. M VL5. -L6. ML7. MA(-L).8. Mv(-M-L)Write the conditional statement in its equivalent disjunetive form."If two triangles are similar, then their coresponding sides are proportional."Write the negation of the given statement in its equivalent conjunctive form."If a square matrix A is singular, then det(4) = 0."10.

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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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Using the letters, A, R, S, and C to abbreviate the simple statements, “America establishes an overseas port,” “Russia establishes an overseas port,” “Sudan government stabilizes,”, and “China lowers cost of materials,” symbolize these statements.1. China lowers cost of materials, but Russia does not establish an overseas port.
Let p and q represent the following statements. p: The tie is black. q: The shoe is red. Write the compound statement p vq in words. Choose the correct answer below. O A. The tie is black or the shoe is red. O B. The tie is black and the shoe is red. O C. The tie is not black or the shoe is red. O D. If the tie is black, then the shoe is red.
Using the symbolic representations given below: p: You are a criminal.p: You are a criminal.q: You break the lawq: You break the law Express the following compound statements in symbolic form. Statement 1: You are a criminal only if you break the law.You are a criminal only if you break the law.A. ∼p→q∼�→�B. q→p�→�C. ∼q→p∼�→�D. p→q�→�E. q→∼p�→∼�F. p→∼q�→∼� Statement 2: If you are not a criminal, you do not break the law.If you are not a criminal, you do not break the law.A. q→∼p�→∼�B. p→∼q�→∼�C. ∼q→p∼�→�D. ∼p→∼q∼�→∼�E. ∼q→∼p∼�→∼�F. ∼p→q∼�→� FILL BLANK: Statement 2 is the ________ of Statement 1.A. contrapositiveB. inverseC. converse Statement 1 and Statement 2 are:A. equivalentB. not equivalent
Let p, q, and r represent the following simple statements. p: I eat bananas. q: I like ice cream. r I like to eat. Write the following compound statement in its symbolic form. If I do not eat bananas then: I do not like ice cream and I do not like to eat. The symbolic form is
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p: Kevin Durant will win the MVP award.q: The Lakers will win the NBA championship. Select the statement below that matches the following symbolic statement: ∼p∨q
Using the symbolic representations given below: p: You are a criminal.p: You are a criminal.q: You break the lawq: You break the law Express the following compound statements in symbolic form. Statement 1: You are a criminal only if you break the law.You are a criminal only if you break the law.A. ∼p→q∼�→�B. q→p�→�C. ∼q→p∼�→�D. p→q�→�E. q→∼p�→∼�F. p→∼q�→∼� Statement 2: If you are not a criminal, you do not break the law.If you are not a criminal, you do not break the law.A. q→∼p�→∼�B. p→∼q�→∼�C. ∼q→p∼�→�D. ∼p→∼q∼�→∼�E. ∼q→∼p∼�→∼�F. ∼p→q∼�→� FILL BLANK: Statement 2 is the ________ of Statement 1.A. contrapositiveB. inverseC. converse Statement 1 and Statement 2 are:A. equivalentB. not equivalent
Use the statements and truth table to determine which statements are equivalent. p: It is a university. q: It offers a degree in electrical engineering. pqpqpq ~p → ~qqp ~q→ ~p TT FL וד F T T T T TF F T F T T F FT T FL T F FL T FF T T T T T T If it offers a degree in electrical engineering, then it is a university. If it is a university, then it offers a degree in electrical engineering. If it offers a degree in electrical engineering, then it is a university. It is a university, and it offers a degree in electrical engineering. If it offers a degree in electrical engineering, then it is a university. If it is not a university, then it does not offer a degree in electrical engineering. If it is a university, then it does not offer a degree in electrical engineering. It is a university, or it offers a degree in electrical engineering.
Tulips The diagram shows the relationship between two sets. Flowers aUse the diagram to write a statement beginning with the word "all," "some," or "no" that illustrates the relationship between the sets. b.Determine if the statement in part (a) is true or false. If it is false, write its negation. a. Choose the correct statement below that illustrates the relationship between the sets. O A. No tulips are flowers. O B. All flowers are tulips. OC. All tulips are flowers. O D. Some flowers are tulips. O E. Some tulips are flowers. b. Is the statement in part (a) true or false? O A. False; its negation is "Some tulips are not flowers." O B. False; its negation is "Some flowers are not tulips." O C. False; its negation is "Some flowers are tulips." OD. False; its negation is "No tulips are flowers." O Time Remaining: 01:58:05 Next MacBook Air 4) 0 9. > FS) F7 esc F2 F4 #3 & * 2$ 4 2 3 5 6. 7 8 9 delete Q W E R Y A S F J K ck C V M N

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