Let P(x) and Q(x) be predicates and suppose D is the domain of x. In 55-58, for the statement forms in each pair, determine whether (a) they have the same truth value for every choice of P(x), Q(x), and D, or (b) there is a choice of P(x), and D for which they have opposite truth values. ∃ x ∈ D , ( P ( x ) ^ Q ( x ) ) , and ( ∃ x ∈ D , P ( x ) ) ^ ( ∃ x ∈ D , Q ( x ) )
Let P(x) and Q(x) be predicates and suppose D is the domain of x. In 55-58, for the statement forms in each pair, determine whether (a) they have the same truth value for every choice of P(x), Q(x), and D, or (b) there is a choice of P(x), and D for which they have opposite truth values. ∃ x ∈ D , ( P ( x ) ^ Q ( x ) ) , and ( ∃ x ∈ D , P ( x ) ) ^ ( ∃ x ∈ D , Q ( x ) )
Solution Summary: The author analyzes whether given two statements have the same truth values for each choice of P(x),Q left (x) and D. Option (b) is true i.e.
Let P(x) and Q(x) be predicates and suppose D is the domain of x. In 55-58, for the statement forms in each pair, determine whether (a) they have the same truth value for every choice of P(x), Q(x), and D, or (b) there is a choice of P(x), and D for which they have opposite truth values.
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MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY