Exercise 9-5 Prove valid (note that these problems are not necessarily in order of difficulty). (11)1.(x)[(Ax ∨ Bx) ⊃ Cx

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Exercise 9-5 Prove valid (note that these problems are notnecessarily in order of difficulty).
(11)1.(x)[(Ax ∨ Bx) ⊃ Cx] p
2. ∼ (∃y)(Cy ∨ Dy) p
/∴ ∼ (∃x)Ax
(13)1. (x)[(Ax ⋅ Bx) ⊃ Cx] p
2. ∼ Cb p
/∴ ∼ (Ab ⋅ Bb)
(15)1. (x)(Hx ⊃ Kx) p
2. (∃x)Hx ∨ (∃x)Kx p
/∴ (∃x)Kx
(17)1. (x)[(Bx ⋅ Ax) ⊃ Dx] p
2. (∃x)(Qx ⋅ Ax) p
3.(x)(∼ Bx ⊃ ∼ Qx) p
/∴ (∃x)(Dx ⋅ Qx)
(19)1. (x)[Px ⊃ (Qx ∨ Rx)] p
2. (x)[(Sx ⋅ Px) ⊃ ∼ Qx] p
/∴ (x)(Sx ⊃ Px) ⊃ (x)(Sx ⊃ Rx)