Question

Show that ¬[∃xA(x)] is equivalent to ∀x[¬A(x)]

Answer 1

\[\neg[\exists xA(x)]\]\[\quad\downarrow\]\[\neg[\exists x]\neg[A(x)]\]\[\quad\downarrow\]\[\forall x [\neg A(x)]\]

Answer 2

is this the way to solve this problem /

Answer 3

Looks right to me. The negation of ∃ is ∀ and then you distributed the negation to A(x).

Answer 4

@joemath314159, @swissgirl , @lgbasallote , @ParthKohli

Answer 5

Yeah, that's right.

Answer 6

how would you know @ParthKohli

Answer 7

Because you have distributed the negation.

Answer 8

is there any other possible intermediate steps?

Answer 9

I don't see any.

Answer 10

ok cool