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Worksheet on Union and Intersection of Sets/4
The intersection of A and B is written "A n B". Formally: {\displaystyle A\cap B=\{x:x\in A\,\land \,x\in B\}} A \cap B = \{ x: x \in A \,\land\, x \in B\} that is x ? A n B if and only if x ? A and x ? B. For example: The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}. The number 9 is not in the intersection of the set of prime numbers {2, 3, 5, 7, 11, ...} and the set of odd numbers {1, 3, 5, 7, 9, 11, ...}.[2] More generally, one can take the intersection of several sets at once. The intersection of A, B, C, and D, for example, is A n B n C n D = A n (B n (C n D)). Intersection is an associative operation; thus, A n (B n C) = (A n B) n C. Inside a universe U one may define the complement Ac of A to be the set of all elements of U not in A. Now the intersection of A and B may be written as the complement of the union of their complements, derived easily from De Morgan's laws: A n B = (Ac ? Bc)c
Last Updated: 5th Aug 2016
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