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1. Let S, the statement: If r and s are rational numbers then r s is a rational number. (a) Let P(x) be the statement "x is a rational number." Analyze the logical form of S1 using P(x). (b) Write the converse of S, in natural English. Converse: IF r.s is a vational number, then r and s rational numbers. Cure (c) Find an example of rational numbers r and s that cause the converse of S1 to be false. r=415 s= (415) ( p (d) Write the contrapositive of S1 in natural English. are IF r.s Is not a rational number, thenrand s not rational numbers. 2. Let S2 be the statement: If x is divisible by either 4 or 6, then x is not prime. (a) Let D(y) be the statement "x is divisible by y" and let P be the statement "x is prime." Analyze the logical form of S2 using D(y) and P.

1. Let S, the statement: If r and s are rational numbers then r s is a rational number. (a) Let P(x) be the statement "x is a rational number." Analyze the logical form of S1 using P(x). (b) Write the converse of S, in natural English. Converse: IF r.s is a vational number, then r and s rational numbers. Cure (c) Find an example of rational numbers r and s that cause the converse of S1 to be false. r=415 s= (415) ( p (d) Write the contrapositive of S1 in natural English. are IF r.s Is not a rational number, thenrand s not rational numbers. 2. Let S2 be the statement: If x is divisible by either 4 or 6, then x is not prime. (a) Let D(y) be the statement "x is divisible by y" and let P be the statement "x is prime." Analyze the logical form of S2 using D(y) and P.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. Let S, the statement: If r and s are rational numbers then r s is a rational number. (a) Let P(x) be the statement "x is a rational number." Analyze the logical form of S1 using P(x). (b) Write the converse of S, in natural English. Convere: IF ris is a vational number, then r andl s Cre rational numbers. (c) Find an example of rational numbers r and s that cause the converse of S1 to be false. .415 5= (415) C (d) Write the contrapositive of S, in natural English. IF rational number, the n rand s r.s IS not a are not rational numberrs. 2. Let S2 be the statement: If x is divisible by either 4 or 6, then x is not prime. (a) Let D(y) be the statement "x is divisible by y" and let P be the statement "x is prime." Analyze the logical form of S2 using D(y) and P. DLY) (b) Write the converse of S2 in natural English. IF x is no F prime, then x is divisible by either 4 or l6 (c) Is the converse of S2 true? If not, find an example of x that makes it false. (d) Write the contrapositive of S2 in natural English. either 4 ov le.
Transcribed Image Text:1. Let S, the statement: If r and s are rational numbers then r s is a rational number. (a) Let P(x) be the statement "x is a rational number." Analyze the logical form of S1 using P(x). (b) Write the converse of S, in natural English. Convere: IF ris is a vational number, then r andl s Cre rational numbers. (c) Find an example of rational numbers r and s that cause the converse of S1 to be false. .415 5= (415) C (d) Write the contrapositive of S, in natural English. IF rational number, the n rand s r.s IS not a are not rational numberrs. 2. Let S2 be the statement: If x is divisible by either 4 or 6, then x is not prime. (a) Let D(y) be the statement "x is divisible by y" and let P be the statement "x is prime." Analyze the logical form of S2 using D(y) and P. DLY) (b) Write the converse of S2 in natural English. IF x is no F prime, then x is divisible by either 4 or l6 (c) Is the converse of S2 true? If not, find an example of x that makes it false. (d) Write the contrapositive of S2 in natural English. either 4 ov le.
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