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Consider the following argument: If I am either sleeping well or doing my assignments, then I will pass the GMath course. Iam sleeping well but I am not doing my assignments. Hence, I will not pass the GMath course Let p = "I am sleeping well.", q = "I am doing my assignments.", and r = "I will pass the GMath course." Which of the following symbolic forms represents the hypothesis (or the conjunction of the premises) in the given argument?

Consider the following argument: If I am either sleeping well or doing my assignments, then I will pass the GMath course. Iam sleeping well but I am not doing my assignments. Hence, I will not pass the GMath course Let p = "I am sleeping well.", q = "I am doing my assignments.", and r = "I will pass the GMath course." Which of the following symbolic forms represents the hypothesis (or the conjunction of the premises) in the given argument?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Consider the following argument: If I am either sleeping well or doing my assignments, then I will pass the GMath course, I am sleeping well but I am not doing my assignments. Hence, I will not pass the GMath course Let p = "I am sleeping well.", q = "I am doing my assignments.", and r = "I will pass the GMath course." Which of the following symbolic forms represents the hypothesis (or the conjunction of the premises) in the given argument? I(p^q) → r] ^ (p V ~q) [(p v q) → r] ^ (p v~q) O Option 1 O Option 2 [(p^q) → r]^ (p ^~q) [(p v q) → r] ^ (p A~q) O Option 3 O Option 4 Assume that p and g are true statements and that r is a false statement. Which of the following statements is NOT true? * (p^q) Vr (1A b) v d Option 1 Option 2 ~p → (~q vr) P+ (q ^r) Option 3 Option 4
Transcribed Image Text:Consider the following argument: If I am either sleeping well or doing my assignments, then I will pass the GMath course, I am sleeping well but I am not doing my assignments. Hence, I will not pass the GMath course Let p = "I am sleeping well.", q = "I am doing my assignments.", and r = "I will pass the GMath course." Which of the following symbolic forms represents the hypothesis (or the conjunction of the premises) in the given argument? I(p^q) → r] ^ (p V ~q) [(p v q) → r] ^ (p v~q) O Option 1 O Option 2 [(p^q) → r]^ (p ^~q) [(p v q) → r] ^ (p A~q) O Option 3 O Option 4 Assume that p and g are true statements and that r is a false statement. Which of the following statements is NOT true? * (p^q) Vr (1A b) v d Option 1 Option 2 ~p → (~q vr) P+ (q ^r) Option 3 Option 4
What are the truth values of x and y respectively if the compound proposition x → (x → y) is false? Suppose p is true, q is true, r is true, s is false. Find the truth value of (~p V s) V (s ^ r) Both False True Both True False False and True True and False Given p → q, which of the following statement/s is or are correct about its Suppose p is false, q is false, s is true. Find the truth value of transformation? (s V p) ^ (q ^ ~s) i. If the given conditional statement is true then its converse, q → p, may perhaps True be true. False ii. The inverse of a given conditional statement is the logical negation of the given conditional statement; that is, ~(p → q) = ~p → ~q. iii. The contrapositive, ~q → ~p, is the converse of the inverse of the given conditional statement. i and ii only Suppose p is true, q is true, r is false, s is false. Find the truth value of (s V p) ^ (~r V ~s) ii onloy True O ii only False O i, ii, and iii
Transcribed Image Text:What are the truth values of x and y respectively if the compound proposition x → (x → y) is false? Suppose p is true, q is true, r is true, s is false. Find the truth value of (~p V s) V (s ^ r) Both False True Both True False False and True True and False Given p → q, which of the following statement/s is or are correct about its Suppose p is false, q is false, s is true. Find the truth value of transformation? (s V p) ^ (q ^ ~s) i. If the given conditional statement is true then its converse, q → p, may perhaps True be true. False ii. The inverse of a given conditional statement is the logical negation of the given conditional statement; that is, ~(p → q) = ~p → ~q. iii. The contrapositive, ~q → ~p, is the converse of the inverse of the given conditional statement. i and ii only Suppose p is true, q is true, r is false, s is false. Find the truth value of (s V p) ^ (~r V ~s) ii onloy True O ii only False O i, ii, and iii
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