Answer to Question #104697 in Discrete Mathematics for Martin

Question

QUESTION 5

In this question you have to construct formal proofs using the natural deduction rules. The Fitch system makes use of these rules.

Remember that De Morgan’s laws and other tautologies are not permissible natural deduction rules. You are also not allowed to use Taut Con, Ana Con or FO Con. It is important to
number your statements, to indicate subproofs and at each step to give the rule that you are using

Question 5.1

Using the natural deduction rules, prove that the following two premises are contradictory:

1 R → (P v Q)
2 R /\ ¬P /\ ¬Q


Question 5.2

Using the natural deduction rules, give a formal proof of

| 1. ¬S
| 2. P → Q
| 3. Q → (R v S)
| 4. P v R
|---
| R


Question 5.3

Prove ∃x[P(x) → ∀yP(y)] from no premises

Answer 1

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