Question

Q.9 Given L = (1, 2, 3, 4], M=(3, 4, 5, 6) and N= (1, 3, 5)
Verify that L-(MU N) = (L-M) N (L-N)​

Answer 1

Step-by-step explanation:

We are given the following tree sets :

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

We are to verify the following :

L - (M U N) = (L - M) ∩ (L - N).

We have

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

So, L.H.S. = L - (M U N) = {1, 2, 3, 4} -  {1, 3, 4, 5, 6} = {2}.

Now,

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

L - N = {1, 2, 3, 4} - {1, 3, 5} = {2, 4}.

So, R.H.S. = (L - M) ∩ (L - N) =  {1, 2} ∩ {2, 4} = {2}.

Therefore, we get

L - (M U N) = (L - M) ∩ (L - N).

Hence verified.