Construct proofs of arguments in QL

Prove the following arguments. Click on selected problems for solutions.

1. (x)(Ax ⊃ Bx), (x)Ax  /// (x)Bx
2. (x)(Sx ⊃ Px) /// ~(∃x)(Sx & ~Px) [Do this without using C.Q.N.]
3. (∃x)(Sx v Px), (x)~Sx /// (∃x)Px
4. (∃x)(Tx & Rx), (∃x)(Tx & Bx), (x)(Rx ⊃ ~Bx) ///~(x)(Tx ⊃ Rx)
5. (x)(Mx ⊃ ~Px), (x)(Sx ⊃ Mx) /// (x)(Sx ⊃ ~Px)
6. (x)(Ax ⊃ ~Bx), (∃x)(Ax & Cx) /// (∃x)(Cx & ~Bx)
7. ~(∃x)(Mx & ~Px), ~(x)(Mx ⊃ ~Sx) /// (∃x)(Sx & Px)
8. (Sa ⊃ (∃x)Px), (x)Sx, /// (∃x)(~Rx v Px)
9. (∃x)(Rx & Sx), (x)(Rx ⊃ ~Px) /// (∃x)(Rx & ~Px)
10. (x)(~Tx ⊃ Ux), (∃x)~Ux ///  (∃x)Tx