Use this key to symbolize the following sentences:
A = Art attends class.
G = Art graduates.
H = Art completes his homework.
L = Art does well in logic.
M = Art does well in math.
P = Art does well in philosophy.
T = Art pays tuition.
W = Art does well in all of his classes.
[22-1] Art does not do well in either logic or math.
[22-2] If Art completes his homework, he does well in both logic and math.
[22-3] If Art does not complete his homework, he does well in neither logic nor math.
[22-4] If Art does well in logic or math, he graduates.
[22-5] Art graduates only if he does well in logic or math.
[22-6] If Art neither pays tuition nor attends classes, he does not graduate.
[22-7] Art does well in logic if he completes his homework and attends class.
[24-1] Explain what the three dichotomies of modality are; and Explain why there are discordance as well as harmony among them.
[24-2] Determine which of the following sentences are tautologies, which are contradictions, and which are contingent.
Show your results in Truth Tables.
1. ~(A & ~A)
2. A V (A --> B)
3. A <--> (B V ~B)
Determine whether the following sentences are logically equivalent or not by showing how Truth Table can be utilized for the analysis (arrow here is used for material conditional):
P --> Q ~Q --> ~P