Let's consider the neutrophic logic cricy values of variables x, , y z (so, for n = 3 ) ( ) 11 1 11 1 *NL x T I F T I F* ( ) , , with 0 , , 1 = ≤≤
( ) 22 2 22 2 *NL y T I F T I F* ( ) , , with 0 , , 1 = ≤≤
NL z T I F T I F ( ) , , with 0 , , 1 = ≤≤ ( 33 3 33 3 )
In neutrosophic logic it is not necessary to have the sum of components equals to 1, as in intuitionist fuzzy logic, i.e. TIF *kk k* + + is not necessary 1, for 1 3 ≤ ≤k As a particular case, we define the tri-nary conjunction neutrosophic operator: 
 ( ) [ ][ ][ ] [ ][ ][ ] 3

$$c_{N}:\left([0,1]\times[0,1]\times[0,1]\right)^{3}\rightarrow[0,1]\times[0,1]\times[0,1]$$
$$c_{{}_{N}}(x,y)=\left(T_{{}_{o}}\,T,I_{{}_{o}}\,I+I_{{}_{o}}\,T,F_{{}_{o}}\,F+F_{{}_{o}}\,I+F_{{}_{o}}\,T\right)$$

If x or y are normalized, then ( , ) *Nc xy* is also normalized. 

If x or y are non-normalized then (, ) *Nc xy x y* = ⋅ where ⋅ means norm. 

Nc is an N-norm (neutrosophic norm, i.e. generalization of the fuzzy t-norm). 
Again, as a particular case, we define the unary negation neutrosophic operator: 
: 0,1 0,1 0,1 0,1 0,1 0,1 [ ][ ][ ] [ ][ ][ ] N n ××→ ××
( )( ) 11 1 111 () , , , , N N *n x n TI F FIT* = = . 
 We take the same Venn Diagram for n = 3 . 
So, 
$$\begin{array}{c}{{N L(x)=\left(T_{1},I_{1},F_{1}\right)}}\\ {{N L(y)=\left(T_{2},I_{2},F_{2}\right)}}\\ {{N L(z)=\left(T_{3},I_{3},F_{3}\right).}}\end{array}$$
Vectors 
3
 T= 
T
T
T
⎛ ⎞ ⎜ ⎟
⎜ ⎟
⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠, 
⎛ ⎞ ⎜ ⎟
⎜ ⎟
⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
 and 
1
⎛ ⎞ ⎜ ⎟
⎜ ⎟
⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
. 
I
I
I
F
F
F
1
1
3
 I= 
3
F= 
2
2
2
3
T = x
F
T
T
⎛ ⎞ ⎜ ⎟ ⎜ ⎟
⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
, 
1
3
 T = y
T
F
T
⎛ ⎞ ⎜ ⎟ ⎜ ⎟
⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
, 
1
⎛ ⎞ ⎜ ⎟ ⎜ ⎟
⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
, 
1
3
T = xy
F
F
T
⎛ ⎞ ⎜ ⎟ ⎜ ⎟
⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
, etc. 
3
T = z
T
T
F
We note 
1
2
2
2
2
and similarly 
⎛ ⎞ ⎜ ⎟
⎜ ⎟
⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
, 
1
⎛ ⎞ ⎜ ⎟
⎜ ⎟
⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
,
1
3
 F = xz
T
F
T
⎛ ⎞ ⎜ ⎟
⎜ ⎟
⎜ ⎟⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
, etc. 
3
 F = x
T
F
F
3
 = y
F
F T
F
1
2
2
2
For shorter and easier notations let's denote No *z w zw* = and respectively N N o o *z w v zwv* =
for the vector neutrosophic law defined previously. Then 
 () ( ) 123 ( , ) , , *NL P c x y TT II IT FF FI FT FIT* = = + ++ + = N