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4 March, 16:07

Using the substitution theorem and the important equivalences (handout) show the following equivalence. Use only one substitution/equivalence rule (such as absorption) per step and justify each step by name'

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  1. 4 March, 19:47
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    Commutative laws: p ∧ q ≡ q ∧ p

    p ∨ q ≡ q ∨ p

    Associative laws: (p ∧ q) ∧ r ≡ p ∧ (q ∧ r)

    (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

    Distributive laws: p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

    p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

    Identity laws: p ∧ t ≡ p

    p ∨ c ≡ p

    Negation laws: p ∨ ∼p ≡ t

    p ∧ ∼p ≡ c

    Double negative law: ∼ (∼p) ≡ p

    Idempotent laws: p ∧ p ≡ p

    p ∨ p ≡ p

    Universal bound laws: p ∨ t ≡ t

    p ∧ c ≡ c

    De Morgan's laws: ∼ (p ∧ q) ≡ ∼p ∨ ∼q

    ∼ (p ∨ q) ≡ ∼p ∧ ∼q

    Absorption laws: p ∨ (p ∧ q) ≡ p

    p ∧ (p ∨ q) ≡ p

    Negations of t and c: ∼t ≡ c

    ∼c ≡ t
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