1.

LetU = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}A = {1, 2, 4, 6}B = {3, 7}C = {1, 3, 6, 7, 9}List all the members of the following set. A ∩ (B ∪ C) LetU = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}A = {2, 4, 6, 8}B = {3, 10}C = {2, 3, 8, 9, 10}List all the members of the following set. A ∪ (B ∩ C)LetU = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}A = {2, 4, 6, 8}B = {3, 9}C = {4, 5, 7, 9, 10}List all the members of the following set. A ∩ B ∪ C

Answer»

(i) A = {1, 2, 4, 6}

B = {3, 7}

And C = {1, 3, 6, 7, 9}

∴ B ∪ C = {1, 3, 6, 7, 9}

Now, A ∩ {B ∪ C} = {1, 2, 4, 6} ∩ {1, 3, 6, 7, 9} = {1, 6}

(ii) A = {2, 4, 6, 8}

B = {3, 10}

C = {2, 3, 8, 9, 10}

∴ B ∩ C = {3, 10}

Now, A ∪ {B ∩ C} = {2, 4, 6, 8} ∪ {3, 10} = {2, 3, 4, 6, 8, 10}

(iii) A = {2, 4, 6, 8}

B = {3, 9}

C = {4, 5, 7, 9, 10}

∴ A ∩ B = ϕ

A ∩ {B ∪ C} = ϕ ∪ C = C = {4, 5, 7, 9, 10}

And B ∪ C = {3, 4, 5, 7, 9, 10}

A ∩ (B ∪ C) = {4}

Thus, (A ∩ B) ∪ C ≠ A ∩ (B ∪ C)

That's why we need to use bracket at right places.


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