Answer :
Answer:
We employ the predicates,
InBox(x):x is in the box
Red(x):x is red
Animal(x):x is an animal
Cat(x):x is a cat
Dog(x):x is a dog
Boy(x):x is a boy
Prize(x):x is a prize
Won(x, y):x won y
to standardise or formalize the above statement.
a. All red things are in the box.
∀x(Red(x)→InBox(x))
b. Only red things are in the box.
∀x(InBox(x)→Red(x))
c. No animal is both a cat and a dog.
¬∃x(Animal(x)∧(Cat(x)∧Dog(x)))
or∀x(Animal(x)→(¬Cat(x)∨ ¬Dog(x)))
d. Every prize was won by a boy.
∀x[Prize(x)→ ∃y(Boy(y)∧Won(y, x))]
e. A boy won every prize.
∃y[Boy(y)∧ ∀x(Prize(x)→Won(y, x))]
Predicate Logic as to do with predicates, it involves propositions that houses variables.
A predicate is an expression of a single or different variables expressed on certain domain. A predicate with variables can be taken as a proposition by placing a value to the variable or by estimating the variable using a quantifier.