a)
x | y | z | _ x |
_ y |
_ z |
xyz | ___ xyz |
_ _ _ x + y+ z |
---|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
On déduit que :
___ xyz |
= | _ _ _ x + y+ z |
: | Théorème de De Morgan sur 3 variables |
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b)
x | y | z | yz |
x + yz | x + y | x + z | (x+y)(x+z) |
---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
On déduit que :
x + yz | = | (x+y)(x+z) | Le OU (+) est distributif sur le ET (.) |
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c)
x | y | _ x |
_ xy |
_ x + xy |
x + y |
---|---|---|---|---|---|
0 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 1 |
On déduit que :
_ x + xy |
= | x + y |
---|