if A={1,2,3,4},B ={3,4,5,6} and C={5,6,7,8} find (AUB)n(AUC)​

Question

if A={1,2,3,4},B ={3,4,5,6} and C={5,6,7,8} find (AUB)n(AUC)​

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Madeline 2 weeks 2021-09-10T21:35:43+00:00 1 Answer 0 views 0

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    2021-09-10T21:37:33+00:00

    Answer :

    (AUB)∩(AUC) = { 1 , 2 , 3 , 4 , 5 , 6 }

    Note:

    ★ Set : A well defined collection of distinct objects is called a set .

    ★ Union of two sets : The union of two sets A and B is the set of all those elements which are either in A or in B or in both .

    → This set is denoted by A U B .

    ★ Intersection of two sets : The intersection of two sets A and B is the set of all those elements which are in common in both A and B .

    → This set is denoted by A ∩ B .

    ★ Difference of sets : The difference of two sets A and B in the order ( also called relative complement of B in A ) is the set of all those elements of A which are not the elements of B .

    → It is denoted by (A – B) .

    Solution :

    → Given : A = { 1 , 2 , 3 , 4 }

    B = { 3 , 4 , 5 , 6 }

    C = { 5 , 6 , 7 , 8 }

    → To find : (AUB)∩(AUC)

    Firstly ,

    Let’s find AUB and AUC .

    Thus ,

    => AUB = { 1 , 2 , 3 , 4 } U { 3 , 4 , 5 , 6 }

    => AUB = { 1 , 2 , 3 , 4 , 5 , 6 }

    Also ,

    => AUC = { 1 , 2 , 3 , 4 } U { 5 , 6 , 7 , 8 }

    => AUC = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }

    Now ,

    (AUB)∩(AUC)

    = { 1,2,3,4,5,6 } ∩ { 1,2,3,4,5,6,7,8 }

    = { 1 , 2 , 3 , 4 , 5 , 6 }

    Hence ,

    (AUB)∩(AUC) = { 1 , 2 , 3 , 4 , 5 , 6 }

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