Question

2. If L= {1,2,3,4} , M={3,,4,5,6} and N ={1,3,5} then verify that L -(M U N)=(L-M) ∩ (L-N).

Answer 1

Given ,

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

first
M U N :-{1,3,4,5,6}
L- (M U N ):- (1,2)

L-M = (1,2)
(L-N)= (1,3)

L-M intersection L-N
(1)

Answer 2

Answer:  The verification is done below.

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.