Question

Use the given predicates and the math editor to write the following sentence in logical form using any appropriate quantifiers and connective. S(x) : X is a student F(x) : x is a faculty member A(x,y) : X Has asked y a question

Answer 1

The sentence 'Every student has asked some faculty member a question' in logical form using given predicates and quantifiers is ∀x (S(x) → ∃y (F(y) ∧ A(x,y))). It utilizes universal and existential quantifiers to establish the relationship expressed in the sentence.

Step-by-step explanation:

To express the sentence 'Every student has asked some faculty member a question' using the given predicates, we would use a combination of universal and existential quantifiers as well as logical connectives.

The logical form of the sentence using the predicates provided would be:

∀x (S(x) → ∃y (F(y) ∧ A(x,y)))

This translates to: for all x, if x is a student, then there exists some y such that y is a faculty member and x has asked y a question.

Predicates and quantifiers are essential parts of this logical expression, representing the relationship between students and faculty members in terms of questions asked.

Answer 2

we have the function f(x)

`f\left(x\right)=\left|(x+1)/(2)\right|`

Remember that

A function is said to be bijective or bijection, if a function satisfies both the injective (one-to-one function) and surjective function (onto function) properties

In this problem

The given function is not a one-to-one function (because for one value of the function f(x) there are two values of x)

see the graph below

therefore

The answer is

Is not a bijective function