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.

Question# 2

Part 1:

Exercise 24:

[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)

Part 2:

Exercise 25:

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

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