Question

Using rules of inference, show that the hypothesis below conclude with b. Give the reason for each step as you show that b in concluded. Each reason should be the name of a rule of inference and include which numbered steps are involved. For example, a reason for a step might be: "Modus ponens using #2 and #3"

Hypotheses given: tavb cvd -an-C -dne

Answer 1

See deduction below

Explanation:

Remember that inference rules allow to make conclusions from given hypotheses. Usually the hypotheses involve the logical connectives (∨,∧,→). A deduction or valid argument is a sequence of applications of inference rules, which results in concluding that some proposition is true.

From your 4 given hypotheses, only the first and third one are necessary to complete the argument.

1) ¬a∧¬c (hypotheses)

2) ¬a (Simplification using 1)

3) a∨b (hypotheses)

4) ∴ b (Modus Tollens using 2 and 3)