Question 2 (a) Give a counter-example to show that the following statement is false. Vx €N Vy €R Vz €R ((x² < y²) v (y² < z²)) → ((x< y) V (y < - (b) Provide the negation of the statement, giving your answer without using any logical negation symbol. Equality and inequality symbols such as =, #, <, > are allowed. 3x €Z vy €N Vz EN ((x + 0) ^ (xy)² = 1) → ((z = 0) V (xy = 1)) (c) Let D be the set D = {-10, –9, –7,-6,-4, -3, -2,0,1,2,3,4,5,6,9,10,12,13,14}. Suppose that the domain of the variablex is D. Write down the truth set of the predicate ((x > 1) – (x is even)) → (x is divisible by 4). (d) Let P, Q, R, S denote predicates. Use the Rules of Inference to prove that the following argument form is valid. Vx (P(x) → (vy QCY) (premise) Vx (R(x) → (3y ~Q)) (premise) 3x (R(x) A S(x)) : Vx -P(x) (premise) (conclusion)
Question 2 (a) Give a counter-example to show that the following statement is false. Vx €N Vy €R Vz €R ((x² < y²) v (y² < z²)) → ((x< y) V (y < - (b) Provide the negation of the statement, giving your answer without using any logical negation symbol. Equality and inequality symbols such as =, #, <, > are allowed. 3x €Z vy €N Vz EN ((x + 0) ^ (xy)² = 1) → ((z = 0) V (xy = 1)) (c) Let D be the set D = {-10, –9, –7,-6,-4, -3, -2,0,1,2,3,4,5,6,9,10,12,13,14}. Suppose that the domain of the variablex is D. Write down the truth set of the predicate ((x > 1) – (x is even)) → (x is divisible by 4). (d) Let P, Q, R, S denote predicates. Use the Rules of Inference to prove that the following argument form is valid. Vx (P(x) → (vy QCY) (premise) Vx (R(x) → (3y ~Q)) (premise) 3x (R(x) A S(x)) : Vx -P(x) (premise) (conclusion)
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 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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