Answer to Question #334275 in Discrete Mathematics for Eve

Question

I.) Identify if the following statements are predicate logic. Give a domain of discourse for each propositional function. 

1. The movie won the Academy Award for the past 2 years.
2. 1 + 3 = 4
3. (x+2)² is a prime number.
4. man is mortal
5. not all people are dishonest.

II.) Convert the given argument into four type of nested quantifier.

"Every Math Teacher is like by some students"

(note: you may take different types of approach in your sentences but the thought of the quantifiers must still be there)

 

Answer 1

Definition: A predicate is a property that is affirmed or denied about the subject (in logic, we say “variable” or “argument”) of a statement.

1. The movie won the Academy award for the past three years is a predicate logic. The domain of discourse here is all movies.

2. 1+3=4 is not a predicate logic. This is because there is no variable or property that is been affirmed or denied according to the definition of predicate. It is just a statement.

3. (x+2)² is a prime number is a predicate logic and the domain of discourse here is the set of numbers.

4.man is mortal.is not a predicate logic. This is because there is no variable or property that is been affirmed or denied according to the definition of predicate. It is just a statement.

5. not all people are dishonest. is a predicate logic. The domain of discourse here is all people.

2part.

My attempt :

"Some student likes x" is $∃(y) \left[\text{student}\left(y\right) ∧ \text{likes}\left(y,x\right)\right]$

So,

"Every teacher is liked by some student" is

$∀(x)\left[\text{teacher}\left(x\right) → ∃(y) \left[\text{student}\left(y\right) ∧ \text{likes}\left(y,x\right)\right]\right]$