(a) Build truth tables for
p ∨ (q ∧ r) and (p ∨ q) ∧ (p ∨ r).
Decide whether it can be said that “OR distributes over AND.” Explain.
(b) Build truth tables for
p ∧ (q ∨ r) and (p ∧ q) ∨ (p ∧ r).
Decide whether it can be said that “AND distributes over OR.” Explain.
(c) Describe how the logical equivalences developed in parts (a) and (b) are related to the set-theoretical equations
X ∪ (Y ∩ Z) = (X ∪ Y) ∩ (X ∪ Z)
and
X ∩ (Y ∪ Z) = (X ∩ Y) ∪(X ∩ Z).
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