Answer:
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.
