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Combien existe-t-il de fonctions logiques de $2$ variables, dans le contexte d’une logique à $3$ valeurs ? Justifier votre réponse

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Find limits involving trigonometric functions

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Q. Combien existe-t-il de fonctions logiques de

2

variables, dans le contexte d’une logique à

3

valeurs ? Justifier votre réponse

Understand the problem: Step $1$ : Understand the problem. $\newline$ In a $3$ -valued logic system, each variable can take one of three values. We need to determine how many different functions can be defined with two variables where each variable can be $0$ , $1$ , or $2$ .
Calculate input combinations: Step $2$ : Calculate the number of possible input combinations. $\newline$ Each of the two variables can take $3$ different values. Therefore, the total number of input combinations for the two variables is $3 \times 3 = 9$ .
Determine output possibilities: Step $3$ : Determine the number of possible outputs for each function. $\newline$ Since the logic system is $3$ -valued, each function can output one of three values ( $0$ , $1$ , or $2$ ) for each input combination.
Calculate total functions: Step $4$ : Calculate the total number of functions. $\newline$ For each of the $9$ input combinations, there are $3$ choices of output. The total number of functions is therefore $3^9$ .
Compute $3^9$ : Step $5$ : Compute $3^9$ . $\newline$ $3^9 = 19683$ .

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