Question

Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate...

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

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.

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