Question

Suppose the domain of the following predicate logic propositions is {1, 2, 3}.

Express the following statements without the use of quantifiers-only conjunctions and negations.

a)

Vx(( 3)P(x)) V P(x)

b)

Answer 1

1. Answer
(P(1) ^ P(2)) V (~P(1) V ~P(2) V ~P(3))

Explanation
(P(1) ^ P(2)): x != 3 which means it should be true for 1 and 2
(~P(1) V ~P(2) V ~P(3)): There is one x for which ~P(x)

2. Answer
(P(1) -> (Q(1, 1) ^ Q(1, 2) ^ Q(1, 3))) && (P(2) -> (Q(2, 1) ^ Q(2, 2) ^ Q(2, 3))) ^ (P(3) -> (Q(3, 1) ^ Q(3, 2) ^ Q(3, 3)))

Explanation
For all values of x = 1, 2, 3 and y = 1, 2, 3

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