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.
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