1. (∃x)(∃y)(Dx • Exb • Dy • Eyb • x≠y)
2. (∀x)(Dx ⊃ Ebx)
-Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
A) (∃y)(Da • Eab • Dy • Eyb • a≠y)
B) Da ⊃ Ebb
C) Da • Eab • Dc • Dcb • a≠c
D) (∃x)(Dx • Exb • Da • Eab • x≠b)
E) Dx ⊃ Ebb

Question

Quizplus · Accepted Answer

The first premise states that there exist two different objects, x and y, such that both are D and both are E to b. The second premise states that for all x, if x is D, then x is E to b. From these, the immediate consequence is that there exists a y such that Da and Eab and Dy and Eyb and a≠y, which matches choice A, as it directly follows from applying the existential instantiation from the first premise and the universal instantiation from the second premise to a specific case.

1 (∃X)(∃y)(Dx • Exb • Dy • Eyb • X≠y)