Let the domain of a variable x be the set of geometric figures in the plane, and let Square(x) be "x is a square" and Rect(x) be "x is a rectangle." For each of the statements in (a), (b), and (c), select the answer that expresses the statement without using quantifiers or variables. Then indicate whether the statement is true or false.

(a)

∃x such that Rect(x) ∧ Square(x)

There are some geometric figures that are both rectangles and squares.All geometric figures are both rectangles and squares.     All geometric figures are rectangles and not squares.There are some geometric figures that are rectangles, but are not squares.For every geometric figure, if the geometric figure is a square then it is also a rectangle.For every geometric figure, if the geometric figure is a rectangle then it is also a square.

This statement is  ---Select--- true false .

(b)

∃x such that Rect(x) ∧ ~Square(x)

There are some geometric figures that are both rectangles and squares.All geometric figures are both rectangles and squares.     All geometric figures are rectangles and not squares.There are some geometric figures that are rectangles, but are not squares.For every geometric figure, if the geometric figure is a square then it is also a rectangle.For every geometric figure, if the geometric figure is a rectangle then it is also a square.

This statement is  ---Select--- true false .

(c)

∀x, Square(x) → Rect(x)

There are some geometric figures that are both rectangles and squares.All geometric figures are both rectangles and squares.     All geometric figures are rectangles and not squares.There are some geometric figures that are rectangles, but are not squares.For every geometric figure, if the geometric figure is a square then it is also a rectangle.For every geometric figure, if the geometric figure is a rectangle then it is also a square.

This statement is  ---Select--- true false .