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QuestionFind the set A∪(B∩C)A \cup (B \cap C) given U={1,2,3,…,7},A={1,2,3,6},B={1,2,7},C={1,2,3,4,5}U=\{1,2,3,\ldots,7\}, A=\{1,2,3,6\}, B=\{1,2,7\}, C=\{1,2,3,4,5\}.

Studdy Solution

STEP 1

Assumptions1. The universal set U is {1,,3,…,7}\{1,,3, \ldots,7\} . The set A is {1,,3,6}\{1,,3,6\}
3. The set B is {1,,7}\{1,,7\}
4. The set C is {1,,3,4,5}\{1,,3,4,5\}

STEP 2

First, we need to find the intersection of sets B and C. The intersection of two sets is the set of elements that are common to both sets.B∩C={xx∈B and x∈C}B \cap C = \{x x \in B \, and \, x \in C\}

STEP 3

Now, plug in the given values for sets B and C to find the intersection.
B∩C={1,2,7}∩{1,2,3,,5}B \cap C = \{1,2,7\} \cap \{1,2,3,,5\}

STEP 4

Calculate the intersection of sets B and C.
B∩C={1,2}B \cap C = \{1,2\}

STEP 5

Now that we have the intersection of sets B and C, we can find the union of set A and the intersection of sets B and C. The union of two sets is the set of all elements that are in either set.
A∪(B∩C)={xx∈A or x∈(B∩C)}A \cup (B \cap C) = \{x x \in A \, or \, x \in (B \cap C)\}

STEP 6

Plug in the values for set A and the intersection of sets B and C to find the union.
A∪(B∩C)={1,2,3,6}∪{1,2}A \cup (B \cap C) = \{1,2,3,6\} \cup \{1,2\}

STEP 7

Calculate the union of set A and the intersection of sets B and C.
A∪(B∩C)={1,2,3,6}A \cup (B \cap C) = \{1,2,3,6\}The set A∪(B∩C)A \cup (B \cap C) is {1,2,3,6}\{1,2,3,6\}.

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