Ask Question
2 November, 07:59

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

+1
Answers (1)
  1. 2 November, 08:05
    0
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “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 ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers