Rewrite each statement into a predicate wff with the domain

Rewrite each statement into a predicate wff with the domain of the whole world. Indicate what each predicate represent. (c) Only science majors take calculus. (d) Not all balls are tennis balls.

Solution

(C) Let us denote

S(x) : x is a science major

C(x) : x take calculus

Then the statement \" Only science majors take calculus \" can be written using predicates as follows

(x) ( S(x) C(x) )

The given statement gives that \" All science majors take calculus \"

(d) Let us denote

B(x) : x is a ball

T(x) : x is a tennis ball

Then the statement \" Not all balls are tennis balls \" can be written using predicates as follows

(x) ( B(x) ¬C(x) )

This statement gives that \" There is a ball that is not a tennis ball \"