BEE3054 Problem Set 1
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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))
2023-02-18