Discrete Math Use quantifiers to express the following state

Discrete Math

Use quantifiers to express the following statements. Define your propositional functions, and let the universe be the set of all things.

a. Cats have fur.

b. Not all animals bark.

c. Dogs sometimes eat cat food.

d. No reptiles have fur.

e. Only cats meow.

Solution

Answer :

a) Consider the given statement \" Cats have fur \"

let us denote C(x) : x is a cat

F(x) : x has fur

then the given statement using quantifier as

x ( P(x) F(x))

b) Consider the given statement \" Not all animals bark \" it means that there exists atleast one animal which is not barking.

let us denote P(x) : x is an animal

B(x) : x barks   

then the given statement using quantifier as

x ( P(x) ¬ B(x))

c)

Consider the given statement \" Dogs sometimes eat cat food \"

let us denote P(x) : x is a dog

F(x) : x eat cat food

then the given statement using quantifier as

x ( P(x) F(x))

d)

Consider the given statement \" No riptile have fur \"

let us denote P(x) : x is a riptile

F(x) : x has fur

then the given statement using quantifier as

x ( P(x) ¬ F(x))

e)

Consider the given statement \" Only cats meow \"

let us denote P(x) : x is a cat

M(x) : x is moew

then the given statement using quantifier as

x ( P(x) M(x) )