Let the premises be the statements "All foods that are healthy to eat do not taste good," "Tofu is healthy to eat," "You only eat what tastes good," "You do not eat tofu," and Cheeseburgers are not healthy to eat."

Identify the rule of inference that is used to arrive at the conclusion from the statements "For all x, if x is healthy to eat, then x does not taste good" and "Tofu is healthy to eat."

(You must provide an answer before moving to the next part.)a. modus tollens b. hypothetical syllogism c. modus ponens d. disjunctive syllogism

c. modus ponens

Explanation:

In propositional logic, we learn that modus ponens is a valid argument and a rule of inference. Modus ponens states that "P implies Q, and if P is true, then Q must be true."

Based on these propositions, we learn that all food that is healthy does not taste good, and tofu is healthy. Therefore,

If all food that is healthy does not taste good,

and tofu is healthy to eat,

then tofu does not taste good.

yes yes yes yes yes yes yes yes yes

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0