Sets L, M, and N are shown. Which of the sets represents L ∪ (M ∩ N) (the union of L with the intersection of sets M and N) ? L = {0, 20, 40, 80, 100} M = {5, 10, 15, 20, 25} N = {10, 20, 30, 40, 50} A) {0, 5, 10, 15, 20, 25, 30, 40, 50, 80, 100} B) {0, 10, 20, 40, 80, 100} C) {20, 40} D) {20}

B

Step-by-step explanation:

L ∪ (M ∩ N) means take "common" between M and N and take "sum of that and L".

Let's find (M ∩ N) (common between M and N):

We know

M = {5, 10, 15, 20, 25}, and

N = {10, 20, 30, 40, 50}

Thus, the common elements are 10 & 20, thus (M ∩ N) = {10,20}

Now we have:

L = {0, 20, 40, 80, 100}

(M ∩ N) = {10,20}

So sum of L and (M ∩ N) are all the unique elements of both the sets. They are 0, 10, 20, 40, 80, 100, or Option B

B) L ∪ (M ∩ N) = {0,10,20,40,80,100}

Step-by-step explanation:

The given sets are;

L = {0, 20, 40, 80, 100}

M = {5, 10, 15, 20, 25}

and

N = {10, 20, 30, 40, 50}

(M ∩ N) are elements in set M and set N

(M ∩ N) = {10,20}

The elements in L ∪ (M ∩ N) are elements in L or M ∩ N or both

L ∪ (M ∩ N) = {0,10,20,40,80,100}

The correct choice is B.