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 true. Truth values that are between $0$ and $1$ indicate varying degrees of truth For instance, the truth value $07$ can be assigned to the statement "Fred is happy" since Fred is happy mos truth value $0\mathrm{.}4$ 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 minimu the two propositions.

What are the truth value of the statements

$($a$)$ Fred and John are happy."

$($b$)$ Neither Fred nor John is happy"