where inf T/\ = min{inf T1, inf T2} sup T/\ = min{sup T1, sup T2} inf I/\ = max{inf I1, inf I2} sup I/\ = max{sup I1, sup I2} 
 inf F/\ = max{inf F1, inf F2} sup F/\ = max{sup F1, sup F2} 

## Neutrosophic Disjunction/Union:

x\/y=(T\/,I\/,F\/), 
where inf T\/ = max{inf T1, inf T2} 
 sup T\/ = max{sup T1, sup T2} inf I\/ = min{inf I1, inf I2} 
 sup I\/ = min{sup I1, sup I2} 
 inf F\/ = min{inf F1, inf F2} 
 sup F\/ = min{sup F1, sup F2} 
Neutrosophic Negation/Complement: 
C(x) = (TC,IC,FC), 
 where TC = F1 inf IC = 1-sup I1 sup IC = 1-inf I1 FC = T1 Upon the above Neutrosophic Conjunction/Intersection, we can define the 

## Neutrosophic Containment:

We say that the neutrosophic set A is included in the neutrosophic set B of the universe of discourse U, 
 iff for any x(TA, IA, FA) ∈A with x(TB, IB, FB) ∈B we have: 
inf TA ≤ inf TB ; sup TA ≤ sup TB; inf IA ≥ inf IB ; sup IA ≥ sup IB; inf FA ≥ inf FB ; sup FA ≥ sup FB. 

3.3. **Remarks**. 

a) The non-standard unit interval ]-0, 1+[ is merely used for philosophical applications, especially when we want to make a distinction between relative truth (truth in at least one world) and absolute truth (truth in all possible worlds), and similarly for distinction between relative or absolute falsehood, and between relative or absolute indeterminacy. 
But, for technical applications of neutrosophic logic and set, the domain of definition and range of the Nnorm and N-conorm can be restrained to the normal standard real unit interval [0, 1], which is easier to use, therefore: 
Nn: ( [0,1] × [0,1] × [0,1] )2 → [0,1] × [0,1] × [0,1] 
and Nc: ( [0,1] × [0,1] × [0,1] )2 → [0,1] × [0,1] × [0,1]. 

b) Since in NL and NS the sum of the components (in the case when T, I, F are crisp numbers, not sets) is not necessary equal to 1 (so the normalization is not required), we can keep the final result un-normalized. 