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QuestionGiven the universal set S={1,2,…,20}S=\{1,2,\ldots,20\} and subsets A={1,3,4,7,10,13,17,18,19,20}A=\{1,3,4,7,10,13,17,18,19,20\} and B={1,2,5,9,10,12,17,20}B=\{1,2,5,9,10,12,17,20\}, find (A∪B)(A \cup B) and (A∩B)(A \cap B).

Studdy Solution

STEP 1

Assumptions1. The universal set is the set of all integers from1 to20. . Set A and B are subsets of.
3. Set A contains the elements {1,3,4,7,10,13,17,18,19,20}.
4. Set B contains the elements {1,,5,9,10,12,17,20}.

STEP 2

The union of two sets, A and B, denoted by A ∪ B, is the set of elements which are in A, in B, or in both A and B.
(A∪B)={xx∈A or x∈B}(A \cup B) = \{x x \in A \, or \, x \in B\}

STEP 3

To find the union of sets A and B, we list all the elements that are in A or B or both, without repetition.
(A∪B)={1,2,3,,5,7,9,10,12,13,17,18,19,20}(A \cup B) = \{1,2,3,,5,7,9,10,12,13,17,18,19,20\}

STEP 4

The intersection of two sets, A and B, denoted by A ∩ B, is the set of elements which are in both A and B.
(A∩B)={xx∈A and x∈B}(A \cap B) = \{x x \in A \, and \, x \in B\}

STEP 5

To find the intersection of sets A and B, we list all the elements that are in both A and B.
(A∩B)={1,10,17,20}(A \cap B) = \{1,10,17,20\} So, the union of sets A and B is {1,2,3,4,5,7,9,10,12,13,17,18,19,20} and the intersection of sets A and B is {1,10,17,20}.

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