Let Q(x) be the statement “x+1>2x”. If the domain consists of all integers, what are these truth values? a) Q(1) b) ∃xQ(x) c) ∀xQ(x) d) ∃x¬Q(x) e) ∀x¬Q(x)

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Let Q(x) be the statement “x+1>2x”. If the domain consists of all integers, what are these truth values? a) Q(1) b) ∃xQ(x) c) ∀xQ(x) d) ∃x¬Q(x) e) ∀x¬Q(x)
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Solution 1

a) Q(1) translates to "1+1>2*1" which simplifies to "2>2". This statement is false.

b) ∃xQ(x) translates to "There exists an x such that x+1>2x". This statement is true for negative integers and zero. For example, if x=-1, the inequality becomes "-1+1 > 2*-1" which simplifies to "0 > -2". This stat Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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