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QuestionFind (A∪B)∪C(A \cup B) \cup C for sets A={1,2,3,4,5,6,7,8}A=\{1,2,3,4,5,6,7,8\}, B={2,4,6,10,12,14}B=\{2,4,6,10,12,14\}, and C={5,7,9,11,13,15}C=\{5,7,9,11,13,15\}.

Studdy Solution

STEP 1

Assumptions1. The set A contains the elements {1,,3,4,5,6,7,8} . The set B contains the elements {,4,614}
3. The set C contains the elements {5,7,9,11,13,15}

STEP 2

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

STEP 3

Now, let's find the union of sets A and B.
A∪B={1,2,3,,5,6,7,8}∪{2,,6,10,12,14}A \cup B = \{1,2,3,,5,6,7,8\} \cup \{2,,6,10,12,14\}

STEP 4

Calculate the union of sets A and B.A∪B={1,2,3,4,,6,7,8,10,12,14}A \cup B = \{1,2,3,4,,6,7,8,10,12,14\}

STEP 5

Now, we need to find the union of the set A∪BA \cup B and set C.(A∪B)∪C={1,2,3,4,5,,7,8,10,12,14}∪{5,7,9,11,13,15}(A \cup B) \cup C = \{1,2,3,4,5,,7,8,10,12,14\} \cup \{5,7,9,11,13,15\}

STEP 6

Calculate the union of the set A∪BA \cup B and set C.
(A∪B)∪C={1,2,3,4,5,6,,8,9,10,11,12,13,14,15}(A \cup B) \cup C = \{1,2,3,4,5,6,,8,9,10,11,12,13,14,15\}So, (A∪B)∪C(A \cup B) \cup C is the set {1,2,3,4,5,6,,8,9,10,11,12,13,14,15}\{1,2,3,4,5,6,,8,9,10,11,12,13,14,15\}.

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