Fuzzy Logic Question Help

Question

so im working on a few questions for my discrete math class and i came up on this question:

The truth value of the conjunction of $2$ propositions in a fuzzy logic is the minimum of the truth values of the $2$ propositions. What are the truth values of the statements "Fred and John is happy" and "Neither Fred nor John is happy".

I am totally confused on how i would do this; I figured I should make a truth table. But i think the whole fuzzy logic thing is getting me confused. Could someone please explain to me (with example) how I would solve this question. Thanks.

Answer 1

If you want an help, you have to submit a "complete" question ...

See :

• Kenneth Rosen, Discrete mathematics and its applications (7th ed), page 16 :

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 a 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,” because Fred is happy most of the time, and the truth value $0.4$ can be assigned to the statement “John is happy,” because John is happy slightly less than half the time.

Use these truth values to solve Exercises 45–47.

Execise 45 : The truth value of the negation of a proposition in fuzzy logic is $1$ minus the truth value of the proposition.

[...]

Execise 46 : The truth value of the conjunction of two propositions in fuzzy logic is the minimum of the truth values of the two propositions. What are the truth values of the statements :

“Fred and John are happy” and “Neither Fred nor John is happy” ?

Thus, the truth value of “Fred and John are happy” is the minimum of the two truth values, i.e.

$min(0.8,0.4)=0.4$.

“Neither Fred nor John is happy” is equivalent to “Fred is not happy and John is not happy"; thus, its truth value is the minimum of the truth values of the two negated statements, i.e.

$min(0.2,0.6)=0.2$.