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1. Consider the predicates with domains all real numbers: P(x): x is a positive number; N(x): x is a negative number: Ox): x is zero. Translate Val-P(x)艹(N(x)田0 (x))) into English. Is this true? Give a counterexample if it is false. a) b) Translate vrlrrりv-wol into English. is this true? Give. countere amplefalse c) Construct the negation of the statement in part b) and write it as a symbolic quantification with negations within the given predicates only; d) Translate the statement from part c) in English. What is its truth value? Give a counterexample if it is false.
2. a) If x and y are real numbers, determine the truth value of Vxay(xty -0). ent in part a) as a symbolic quantification with no negations. c) What is the truth value of Vx3y(y-1)? Give a counterexample if it is false. d) Write the negation of the statement in part c) as a symbolic quantification with no negations. e) If x, δ, ε are positive real numbers, translate vaac < δ-+ x2 < ε) in English.
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