# Difference between revisions of "Manuals/calci/COMPLEMENT"

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*So complement os A is defined by:The relative complement of A with respect to a set B, also termed the difference of sets A and B, written <math>\frac{B}{A}</math>, is the set of elements in B but not in A. | *So complement os A is defined by:The relative complement of A with respect to a set B, also termed the difference of sets A and B, written <math>\frac{B}{A}</math>, is the set of elements in B but not in A. | ||

*When all sets under consideration are considered to be subsets of a given set U(Universal Set), the absolute complement of A is the set of elements in U but not in A. | *When all sets under consideration are considered to be subsets of a given set U(Universal Set), the absolute complement of A is the set of elements in U but not in A. | ||

+ | |||

+ | ==Examples== | ||

+ | #COMPLEMENT([19,14,17,23,45,89],[89,90,14,45,32,10,1]) = 90 32 10 1 | ||

+ | #COMPLEMENT([1,2,3,4,5,6,7,8,9,10],[8,9,10,11,12,13,14,15,16]) = 11 12 13 14 15 16 | ||

+ | #COMPLEMENT([67,12,20,56,10,18],[67,12,20,56]) = Null | ||

+ | |||

+ | ==See Also== | ||

+ | *[[Manuals/calci/COMPLEX | COMPLEX ]] | ||

+ | [[Manuals/calci/ISCOMPLEX | ISCOMPLEX ]] | ||

+ | *[[Z_API_Functions | List of Main Z Functions]] | ||

+ | *[[ Z3 | Z3 home ]] | ||

+ | |||

+ | ==References== | ||

+ | [https://en.wikipedia.org/wiki/Complement_(set_theory) Complement] | ||

+ | *[[Z_API_Functions | List of Main Z Functions]] | ||

+ | *[[ Z3 | Z3 home ]] |

## Revision as of 14:17, 5 April 2017

**COMPLEMENT (B,A)**

- and are any two sets.

## Description

- This function shows the complement of the given sets.
- In , and are two sets.
- In Set theory,the complement of a set A refers to elements not in A and which will be in the set B(Universal set).
- So complement os A is defined by:The relative complement of A with respect to a set B, also termed the difference of sets A and B, written , is the set of elements in B but not in A.
- When all sets under consideration are considered to be subsets of a given set U(Universal Set), the absolute complement of A is the set of elements in U but not in A.

## Examples

- COMPLEMENT([19,14,17,23,45,89],[89,90,14,45,32,10,1]) = 90 32 10 1
- COMPLEMENT([1,2,3,4,5,6,7,8,9,10],[8,9,10,11,12,13,14,15,16]) = 11 12 13 14 15 16
- COMPLEMENT([67,12,20,56,10,18],[67,12,20,56]) = Null