Question

Question 34
6. Marks
If there are 400 elements in consideration, set A has 100 elements. Set B
has 150 elements, and 75 are the common elements. Find how many
elements is neither in A nor in B. Draw the Venn diagram for supporting
your answer.​

Answer 1

Answer:

A=100, B=150, Common elements=75 ,Total elements=400

Total elements considered in both A and B=100+150-75=225

No of elements neither in A nor in B = 400-175=225

Ans=225

Answer 2

Answer:

225 elements is neither in A nor in B.

Step-by-step explanation:

Given: Total number of elements, U = 400

⇒ n(U) = 400

Number of elements in set A = 100

⇒ n(A) = 100

Number of elements in set B = 150

⇒ n(B) = 150

Number of common elements in set A and B = 75

⇒ n(A ∩ B) = 75

Using formula, compute total number of elements in set A and B,

⇒ n(A ∪ B) = n(A) + n(B) - n( A ∩ B)

Substitute all the given the values, we get

⇒ n(A ∪ B) = 100 + 150 -75

⇒ n(A ∪ B) = 175

Hence, total number of elements in set A and B are 175.

Now,

Number of elements neither in A nor B = n(U) - n(A ∪ B)

⇒ 400 - 175

⇒ 225

Therefore, 225 elements is neither in A nor in B.

For the diagram shown below, U is universal set which contains all the sets.

SPJ3