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A). If A, B and C are true statements and X,Y, and Z are false statements, determine which of the following are true, using the truth tables for the horseshoe, the dot, the wedge, and the curl. Please write each step of every problem.

1.[( A . X) V ( ~A .~X)] ⊃[( A ⊃ X) . (X ⊃A)]

2. {[ A ⊃ ( B ⊃ C)] ⊃ [(A . B)⊃ C]} ⊃[(Y ⊃ B) ⊃( C ⊃ Z)]

3. {[ X ⊃ Y) ⊃ Z] ⊃[ Z ⊃( X⊃ Y)]} ⊃[(X ⊃ Z) ⊃Y]

4. [( A . X) ⊃ Y] ⊃ [(A ⊃X) . (A ⊃Y)]

5. [ A ⊃ (X . Y)] ⊃[( A ⊃ X) V ( A ⊃ Y)]

B). If A and B are known to be true, and X and Y are known to be false, but the truth values of P and Q are not known, of which of the following statements can you determine the truth values? * do each problem 2 ways, one time being true, another time being false. * show all work.

1. ~( A . P) ⊃(~ A V~P)

2. ~( P . X) ⊃~( P V ~X)

3. ~(X V Q) ⊃( ~X . ~Q)

4. [P ⊃( A V X)] ⊃[( P ⊃ A) ⊃ X]

5. [ Q V (B . Y)] ⊃ [( Q V B) . (Q V Y)]

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