QL Truth-Tree Exercise

Test the following arguments for validity:

1. (x)(Rx ⊃ Tx),  (∃x)(Tx & ~Sx) /// (x)(~Tx ⊃  Sx)

2. (∃x)(Lx & Mx), (∃x)(Px & ~Lx) /// (x)(Px  ⊃  ~Mx)

3. (x)((Rx & Sx) ⊃ ~Gx), (∃x)(Gx & ~Rx) /// (x)(Sx ⊃ Rx)

4. (x)(Ax ⊃ Rx) /// (∃x)(Ax & Rx)

5. (x)Px ⊃ (∃x)Gx, (x)~Gx /// (∃x)~Px

6. (x)(Ax ⊃ Bx), (∃x)(Cx & ~Bx) /// (x)(Ax v Cx)

7. (∃x)Rx v (∃x)Sx, (x)~Rx /// ~(x)~Sx

8. ~(x)~Tx, ~(∃x)Tx & Ga /// (x)(Fx ⊃ Tx)

9. (x)(Sx ⊃ Px) /// (∃x)(Sx & Px)

10. (x)(Sx ⊃ Px) /// ~(∃x)(Sx & ~Px)

11. (∃x)(Ax & ~Bx), (∃x)(Bx & ~Cx), /// ~(x)(Ax ⊃ Cx)

Test the logical status of the following propositions:

1. Fa ⊃ (∃x)Fx

2. (∃x)(Tx & ~Sx) ⊃ (∃x)~(~Sx ⊃ ~Tx)

3. ~(x)~Cx ≡ (∃x)Cx

4. (x)(Fx & Gx) ⊃ (x)(Fx ⊃ Gx)

5. (x)(Ax ⊃ Bx) ⊃ ((x)Ax ⊃ (x)Bx)

Construct syllogisms, translate them into QL, and test them for validity using the truth-tree method. Then double check your answers by testing the syllogisms for validity using one of the three methods you learned in the Traditional Logic chapter.