If P(x) is a predicate and the domain of x is the set of all real numbers, let R be “∀x ∈ Z, P(x),” let S be “∀x ∈ Q, P(x),” and let T be “∀x ∈ R, P(x).”
a. Find a definition for P(x) (but do not use “x ∈ Z”) so that R is true and both S and T are false.
b. Find a definition for P(x) (but do not use “x ∈ Q”) so that both R and S are true and T is false.
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