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