Question

If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have?
NCERT Solutions for Class 11th Mathematics Chapter 1 Exercise 1.6 4

Answer 1

Answer: -
      
n(S) = 21 n(T) = 32
S ∩ T =11
S ∪ T = ?

we know that ,
    
S ∪ T = n(S) + n(T) - S ∩ T Substituting the values ,we get
      
S ∪ T = n(S) + n(T) - S ∩ T                 =21 + 32 - 11 = 53 - 11 = 42

Hope this helps You!!!

Answer 2

n(S U T) = 42

Given:

n(S) = 21

n(T) = 32

n(S ⋂ T) = 11

To Find:

n(S U T)

Calculating:

The formula that is used to calculate the union of sets:

n(S U T) = n(S) + n(T) - n(S ⋂ T)

Substituting all the values that are known to us in this formula we get:

n(S U T) = 21 + 32 - 11

n(S U T) = 53 - 11

n(S U T) = 42

Therefore, n(S U T) = 42.