Question

Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) B(x): x is a ball R(x): x is round $(x): x is a soccer ball a. All balls are round. b. Not all balls are soccer balls. c. All soccer balls are round. d. Some balls are not round. e. Some balls are round but soccer balls are not f. Every round ball is a soccer ball.

Discrete math structures

Answer 1

(a) (∀x)B(x)→[R(x)]

(b) (∃x)B(x)∧~[S(x)]

(c) (∀x)S(x)→[R(x)]

(d) (∃x)B(x)∧~[R(x)]

(e) ∀x,(B(x)∧R(x))∧(∀x,(B(x)∧S(x))→R(x))

(f)  ∀x,(B(x)∧R(x))→(B(x)∧S(x))