Question

4. Let the domain of x be the set of geometric figures in the plane, and let S(x) be "x is a square" and R(x) be "x is a rectangle." Rewrite each statement in English without quantifiers or variables, and say whether it is true or false a. (Bx)(Rx) A S(x) b. (x)(S(x) Rx))

Answer 1

Solution:

Given that: - x rightarrow set of geometric figures square (x) rightarrow 'x' is a square rect(x) rightarrow 'x' is a rectangle. a) (there exist x)(R(x) ^s(x)) there exist x such that rect (x)^square (x) therefore there are some rectangles which are squares b) (for all x)(s (x) rightarrow R(x)) for all x, square (x) rightarrow rect (x) therefore every square is a rectangle.