If some journalists are not respectable, then all journalists on the web have work to do. Some journalists on the web lack assignments. It is not the case that something without an assignment has work to do. So all journalists are respectable.
-Which of the following is the best translation into M of this argument?
A) (∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
(∃x)(∼Ax • Wx) / (∀x)(Jx ⊃ Rx)
B) (∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
∼(∃x)(∼Ax • Wx) / (∀x)(Jx ⊃ Rx)
C) ∼(∃x)(Jx • Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
∼(∃x)(∼Ax • Wx) / (∀x)(Jx ⊃ Rx)
D) ∼(∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • ∼Ax]
∼(∃x)(Ax • Wx) / (∀x)(Jx ⊃ Rx)
E) (∃x)(Jx • ∼Rx) ⊃ (∀x)[(Jx • Ix) ⊃ Wx] (∃x)[(Jx • Ix) • Ax]
∼(∃x)∼(Ax • Wx) / (∀x)(Jx ⊃ Rx)

Question

Quizplus · Accepted Answer

The correct translation reflects the structure of the argument: some journalists are not respectable implies all journalists on the web have work to do; some journalists on the web lack assignments; it is not the case that something without an assignment has work to do; therefore, all journalists are respectable. Option B accurately captures these premises and the conclusion using logical notation.

If Some Journalists Are Not Respectable, Then All Journalists on the Web