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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 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 truthvalues to solve below exercise.

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?”
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truth value of "Fred is happy" = 0.8
truth value of "Fred is not happy" = 0.2

truth value of "John is happy" = 0.4
truth value of "John is not happy" = 0.6

Truth value of "Fred and John are happy" is min(0.8, 0.4) = 0.4


"Neither Fred nor John is happy" can be written as
"Fred is not happy and John is not happy"
its truth value is min(0.2, 0.6) = 0.2

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