1. {x: x is an integer neither positive nor negative} is ________a) Empty setb) Non-empty setc) Finite setd) Non- empty and Finite set

To determine the nature of the set {x: x is an integer neither positive nor negative}, we need to analyze the definition provided.

1. An integer is a whole number that can be positive, negative, or zero.
2. The set specifies that x is neither positive nor negative.

The only integer that is neither positive nor negative is zero.

Therefore, the set {x: x is an integer neither positive nor negative} contains only the element zero.

Now, let's evaluate the options:

a) Empty set: This is incorrect because the set contains the element zero. b) Non-empty set: This is correct because the set contains one element, zero. c) Finite set: This is also correct because the set contains a finite number of elements (specifically, one element). d) Non-empty and Finite set: This is the most accurate description because the set is both non-empty and finite.

Thus, the correct answer is:

d) Non-empty and Finite set