Question

Prove that the following arguments are invalid. Use the method of interpretation to do this. Thank...

Prove that the following arguments are invalid. Use the method of interpretation to do this. Thank you.

(1)

1. (∃x)(Ax ⋅ Bx)

2. (∃x)(Bx ⋅ Cx)
/∴ (∃x)(Ax ⋅ Cx)

(3)

1. (∃x)(Ax ⋅ ~ Bx)

2. (∃x)(Ax ⋅ ~Cx)

3. (∃x)(~ Bx ⋅ Dx)

/∴ (∃x)[Ax ⋅ (~ Bx ⋅ Dx)]

(5)

1. ( ∃x)(Px ⋅ ~ Qx)

2. (x)(Rx ⊃ Px)

/∴ ( ∃x)(Rx ⋅ ~ Qx)

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