1. (∃x)(Ax • Bx • Cax)
2. (∀x)[(Ax • Cax) ⊃ x=d]
-Which of the following propositions is an immediate (one-step) consequence in F of the given premises?
A) (Ab • Cba) ⊃ b=d
B) Ab • Bb • Cab
C) (Aa • Caa) ⊃ x=d
D) Ax • Bx • Cax
E) (Ax • Cax) ⊃ b=d

Question

Quizplus · Accepted Answer

The first premise states that there exists an x such that Ax, Bx, and Cax are all true. The second premise is a universal statement that for all x, if Ax and Cax are true, then x equals d. However, the immediate consequence of the first premise alone, without needing to apply the second, is that there is a specific instance where Ab, Bb, and Cab are true, which matches choice B. This is because we can substitute 'b' for 'x' in the existential quantifier's scope, indicating that there exists at least one such entity (in this case, represented by 'b') for which all three conditions are met. The other options either misapply the premises or involve steps beyond a single, immediate consequence.

1. (∃X)(Ax • Bx • Cax)