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U = {a, b, c, d, e}    A = {d, e}    B = {a, b, c}.Which one of the following statements regarding the given sets is FALSE?a.A’ – U = {d, e}b.(A ⋂ B) + U = {a, b, c, d, e}c.(U ⋂ B’) = B’d.(U – A) + B = U – (A + B)

Question

U = {a, b, c, d, e}    A = {d, e}    B = {a, b, c}.Which one of the following statements regarding the given sets is FALSE?a.A’ – U = {d, e}b.(A ⋂ B) + U = {a, b, c, d, e}c.(U ⋂ B’) = B’d.(U – A) + B = U – (A + B)

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Solution

The false statement among the given options is:

a. A’ – U = {d, e}

Explanation:

A' represents the complement of set A in the universal set U. So, A' = U - A = {a, b, c}.

Subtracting U from A' would result in an empty set, not {d, e}. Therefore, statement a is false.

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