Translate each of these statements into logical expressions by using quatifiers and predicates with one or two variables. (a) A student in our discrete math class has lived in Florida. (b) There is a student in our discrete math class who got the perfect grade in Midterm I. (c) Everyone in our class loves discrete math. (d) There is a student in our class who has been to every state in the US. (e) There is a student in our class who has been to every city of at least one state in the country.

a) , b) , c) , d) , e)

Step-by-step explanation:

a) x - A student, M - Set of students of discrete math class, G - has lived in, y - Florida, U - Set of states of the United States of America.

b) x - A student, M - Set of students of discrete math class, y - A perfect grade, H - Midterm I.

c) x - A student, M - Set of students of discrete math class, I - loves discrete math.

d) x - A student, M - Set of students of discrete math class, J - has been in, y - a state, U - Set of states of the United States of America.

e) x - A student, M - Set of students of discrete math class, J - has been in, y - a city, V - At least one state of the United States of America, U - Set of states of the United States of America.

y = - (x - 3)(x + 5)

Step-by-step explanation:

Given the x- intercepts are x = 3 and x = - 5 then the corresponding factors are

(x - 3) and (x + 5)

The equation is the the product of the factors, that is

y = a(x - 3)(x + 5)  ← a is a multiplier

To find a substitute (- 1, 8) into the equation

8 = a(- 1 - 3)(- 1 + 5) = a(- 4)(4) = - 16a ( divide both sides by - 16 )

- = a

Then

y = - (x - 3)(x + 5) ← in factored form