Fuzzy logic is used in artificial intelligence. in fuzzy logic, a proposition has a truth value that is a number between 0 and 1 inclusive. a proposition with a truth value of 0 is false and one with truth value of 1 is true. truth values that are between 0 and 1 indicate varying degrees of truth. for instance, the truth value 0.8 can be assigned to the statement "fred is happy.'' since fred is happy most of the time, and the truth value 0.35 can be assigned to the statement "john is happy.'' since john is happy slightly less than half the time. the truth value of the negation of a proposition in fuzzy logic is 1 minus the truth value of the proposition. the truth value of a conjunction of two propositions in fuzzy logic is the minimum of the truth values of the two propositions. what are the truth value of the statements: (a) ``fred and john are happy.'' and (b) ``neither fred nor john is happy.''

Truth value for "Fred and John are happy" : 0.35

Truth value for "Neither Fred nor John is happy" : 0.2

Step-by-step explanation:

For (a) part:

We know that the truth value of a conjunction of two propositions (in fuzzy logic) is the minimum of the truth values of each proposition. In our case, the truth value that corresponds to the statement "Fred is happy" is 0.8 and the truth value that corresponds to "John is happy" is 0.35. The minimum of these values (0.8, 0.35), is 0.35, which corresponds to the truth value of the statement "Fred and John are happy".

For (b) part:

In order to answer this part of the problem, first we need to find the truth values of the negations of the initial propositions ("Fred is not happy" and "John is not happy"), which we do by calculating 1 minus the truth value of the initial proposition. Therefore, the truth value of the negations are:

Truth value of "Fred is not happy" (negation of "Fred is happy") is 1 - 0.8 = 0.2

Truth value of "John is not happy" (negation of "John is happy") is 1 - 0.35 = 0.65

Finally, in order to find the conjunction of these negations, we just find the minimum of these values, which is: 0.2.

The question is incomplete. Here is the complete question

Read the excerpt from "Bone Detective," by Lorraine Jean Hopping.

Diane stood in front of a mirror and stuck out her tongue. It looked like a rosy pink welcome mat to her delicate insides. Her usual rubber mold formula was out of the question—too toxic. She wondered, What is safe to swallow, fast and easy to apply, and hardens quickly into a firm mold?

One of her horse-riding pals, a veterinarian named Mary Wright, had the alginate. Mary told Diane that alginate was a pink gummy material used to make molds of teeth. If it was safe for pets, it should be safe for a tiger.

And people, too, Diane thought.

Based on the details in this excerpt, the author would most agree that Diane France is

generous and friendly.

cautious and fearful.

unwise and hasty.

curious and resourceful.

Cautious and fearful

Explanation:

According to the excerpt gotten from the book "Bone detective" Diane is very worried about the state of her teeth. She needs a new mold formular for her teeth as the previous one that she uses is very toxic and no longer suitable to her.

Diane needs a new mold formular that would be easy to apply, be able to solidify within a short period of time and safe for her body.

A close friend of hers Mary Wright suggested a new mold formular to her. Mary is a veterinarian who specializes in treating animals. Mary told her that the alignate formular has been successfully used for her pets.

Diane is scared on what formular to use as she needs to be very careful in choosing the right one that will not cause more harm to her teeth.