Express the statement as a disjunction in dnf, Mathematics

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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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