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) is “x is a ball.”

R(x) is “x is round.”

S(x) is “x is a soccer ball.”

1) some balls are round but soccer balls are not

2) if soccer balls are round, then all balls are round

Answer 1

the above are the predicate logics for the above english statements.

In the first statement

Some balls are round shown as

There exists x(b(x)^r(x)) then but soccer balls are not round

Shown as there exists x (s(x) ^r(x)')

-- in the second statement

If the soccer balls are round shown as

Forall x (s(x) -> r(x) then all are round will be represented as

Forall x(b(x) -> r(x)

In the predicate if there is 'some' in the statement max times we use thereexists and ^ symbol to represent in predicate logic

In the statement we encounter 'if then' then we must use -> in the predicate logic.