Note: this question has two parts. Select only one response for each part. Consi

Question

Note: this question has two parts. Select only one response for each part.

Consider the following expression.

¬( ((f(x)<)(g(x)<)))¬( ((f(x)<)(g(x)<)))

Part 1. To which of the following is the above expression logically equivalent?

((f(x)<)(g(x))) ((f(x)<)(g(x)))

((f(x)<)(g(x)>)) ((f(x)<)(g(x)>))

((g(x)<)(f(x)<)) ((g(x)<)(f(x)<))

((f(x)<)(g(x))) ((f(x)<)(g(x)))

Part 2. Translate the original expression from quantifiers and logical symbols to an English sentence.

There are no combinations of and such that if f(x) < , then g(x) < .

It is not the case that for all , there is some such that if f(x) < , then g(x) < .

It is not the case that for all , there is some such that f(x) < and g(x) < .

For all , there is no such that if f(x) < , then g(x) < .

Explanation / Answer

A) is logically equivalent to given thing that is for all delta there exists an epsilon such that f(x) < epsilon implies g(x) is greater than or equal to delta.

B)it is not the case that for all epsilon there is some delta such that if f(x) is leass than epsilon then g(x) is less than delta

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