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State the following statement as a disjunction (in DNF) as well using quantifiers:
There does not exit a woman who has taken a flight on each airline in the world.
Ans: Let us describe the propositions.
Woman (x): "x is woman"
Flight (x, y): "x has taken flight on every airline y in world".
Now the following statement can be expressed as
~[∃x Woman (x) ∧ ∀y Flight (x, y)]
= ~∀y ∃x [Woman (x) ∧ Flight (x, y)]
= ∃y ∀x [~Woman (x) ∨ ~Flight (x, y)]
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Prove the subsequent Boolean expression: (x∨y) ∧ (x∨~y) ∧ (~x∨z) = x∧z Ans: In the following expression, LHS is equal to: (x∨y)∧(x∨ ~y)∧(~x ∨ z) = [x∧(x∨ ~y)] ∨ [y∧(x∨
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