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Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6}

Question:

Given L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}. Verify that L–(M∪N) = (L–M)∩(L–N).

Solution:

According to the question,

L = {1, 2, 3, 4}, M = {3, 4, 5, 6} and N = {1, 3, 5}

To verify:

L – (M ∪ N) = (L – M) ∩ (L – N)

M = {3, 4, 5, 6}, N = {1, 3, 5} ⇒ M ∪ N = {1, 3, 4, 5, 6}

L = {1, 2, 3, 4} and M ∪ N = {1, 3, 4, 5, 6}

⇒ L – (M ∪ N) = {2}………………(i)

L = {1, 2, 3, 4} and M = {3, 4, 5, 6} ⇒ L – M = {1, 2}

L = {1, 2, 3, 4} and N = {1, 3, 5} ⇒ L – N = {2, 4}

L – M = {1, 2} and L – N = {2, 4}

⇒ (L – M) ∩ (L – N) = {2}………………(ii)

From equations (i) and (ii),

We have,

L – (M ∪ N) = (L – M) ∩ (L – N)

Hence verified

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