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Problem Set 1

Module number: BEE3054

Problem 1. Check whether the following sentences are logically equivalent

P ∧ (Q ∨ R)

and

(P ∧ Q) ∨ (P ∧ R)

Problem 2. Classify the following claims as being either deductive or inductive:

1. Swans are often fed down by the quay, so there is likely a swan at the quay right now.

2. I bring my umbrella when it is raining, and I have my umbrella with me, so it is raining.

3. I bring my umbrella when it is raining, and it is raining, so I have my umbrella

4. The sun has risen every day of my life, so the sun will rise tomorrow.

Problem 3. Use both a list and a syntax tree to demonstrate that the following is a well formed formula

¬(((P ∨ Q) ↔ (Q ∧ S)) → T)

Problem 4. Is the following formula satisfifiable? Is it a tautology? Is it a contradiction?

((P → Q) ∧ (R → S)) ↔ (P → (¬S))