determine whether the given formula is a logical truth of M or not. If it is not a logical truth, select a false valuation.
-(∃x)(Ix • Jx) ⊃ [(∀x)Ix ⊃ (∀x)Jx]
A) Logical truth
B) Not a logical truth. False valuation in a domain of 2 members, in which: Ia: False Ja: True
Ib: True Jb: False
C) Not a logical truth. False valuation in a domain of 2 members, in which: Ia: True Ja: True
Ib: True Jb: False
D) Not a logical truth. False valuation in a domain of 2 members, in which: Ia: True Ja: True
Ib: False Jb: False
E) Not a logical truth. False valuation in a domain of 2 members, in which: Ia: True Ja: False
Ib: True Jb: False

Question

Quizplus · Accepted Answer

The formula is not a logical truth because there exists a valuation where the antecedent is true, but the consequent is false. In option C, (∃x)(Ix • Jx) is true because there is an x (specifically 'a') for which both Ix and Jx are true. However, (∀x)Ix ⊃ (∀x)Jx is false because while (∀x)Ix is true, (∀x)Jx is false due to Jb being false.

Determine Whether the Given Formula Is a Logical Truth of M