Module 2 Homework - Logic 1. 1. (P \cdot Q) \to C 2. P \cdot (D \cdot Q) \cdots P \cdot C 2. 1. L \to (B \cdot C) 2. C \to (D \cdot E) 3. L \cdots B \cdot E 3. 1. (A \lor B) \to C 2. C \to (D \lor E) 3. A \cdot \neg D \cdots E 4. 1. (P \equiv Q) \to T 2. L \to (P \equiv Q) 3. \neg T \cdot Q \cdots \neg L \lor M 5. 1. A \to (B \to C) 2. A \to (D \to E) 3. A \cdot (B \lor D) \cdots C \lor E
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Assignment 1.1 Q1 Prove by truth table De Morgan's laws of logical equivalence. Q2 Prove by truth table Absorption laws of logical equivalence. Q3 Use logical equivalences to reduce the statement and find if the equivalency is true or false? ~((~p ∧ q) ∨ (~p ∧ ~q)) ∨ (p ∧ q) ≡ p Q4 Use logical equivalences to reduce the below expression involving conditionals: (p → (q → r)) ↔ ((p ∧ q) → r)
Adi S.
Truth Table 1 | p | ~p | ~(~p) | |---|---|---| Truth Table 2 | p | ~p | p V ~p | p ^ ~p | |---|---|---|---| | T | | | | | F | | | | Truth Table 3 | p | q | ~q | p ^ ~q | p -> q | ~(p -> q) | |---|---|---|---|---|---|
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In each of 1-4, construct a Truth Table: 1. (~P v Q) -> (~Q ^ P) 2. (P -> Q) -> (P v ~R) 3. [(P v Q) ^ R] -> [(P ^ R) v Q] 4. ~[((P -> Q) ^ (~Q v R)) ^ (~R ^ P)]
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