Question: Consider the propositions (x U)(x^2 - 4 = 0) and (x U)(x^2 - 2 = 0), where U is some universe of discourse.

Consider the propositions (∃x ∈ U)(x^2 - 4 = 0) and (∃x ∈ U)(x^2 - 2 = 0), where U is some universe of discourse.

(a) Do these propositions have the same truth value if the universe of discourse is the set of real numbers? 

(b) Provide an example of a universe of discourse such that the propositions yield different truth values. 

(c) What can you conclude about the logical equivalence of these propositions?

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