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Use an element argument to prove each statement. Assume that all sets are subsets of a universal set U.

For all sets A, B, andC, if A ⊆ B then A∪C ⊆ B∪C

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  1. Today, 08:05
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    Answer with explanation:

    We are asked to prove the statement,

    For all sets A, B, and C, if A ⊆ B then A∪C ⊆ B∪C

    Let us consider set A as:

    A={1,3,4,5}

    and B={1,2,3,4,5,6,7}

    Clearly we may observe that A is a subset of B.

    (Since, all the elements of set A are contained in set B.

    Hence, A is a subset of B)

    Now let us consider set C as:

    C={1,2}

    Hence,

    A∪C={1,2,3,4,5}

    and

    B∪C={1,2,3,4,5,6,7}

    Still we observe that:

    A∪C ⊆ B∪C

    Since all the elements of the set A∪C are contained in the set B∪C.
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