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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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Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc for all c. (b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
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