Test #5
Test #5 will have three parts. In the first part (60%), you will be asked to derive the conclusions of three arguments using our rules of inference for M. In the second part (30%), you will be asked to show two arguments invalid using the method of expansion into finite domains. The third part of the test (10%) includes an argument which is not labelled as either valid or invalid. You should either prove it, if it is valid, or provide a counter-example, if it is invalid.
Here is a practice test, a little longer than the real thing.
3.5: 4, 16, 23
3.7: 6, 9, 31Determine if the following argument is valid or invalid. Provide a proof (either a derivation or a counter-example) in either case.
1. (∃x)(Ax ∙ Bx)
2. (∃x)(Ax ∙ Cx)
3. (∀x)(Bx ⊃ ∼Cx)
4. (∀x)(Dx ⊃ ∼Ax) / (∀x) ∼Dx
Here is a solution to the last problem. Here are some more practice problems and their solutions.