Out of 32 persons, 30 invest in National savings Certificates and 17 invest in shares. What is the number of persons who invest in both?a)13b)15c)17d)19Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
- Total number of persons = 32
- Number of persons who invest in National Savings Certificates = 30
- Number of persons who invest in shares = 17

To find:
The number of persons who invest in both National Savings Certificates and shares.

Solution:
To find the number of persons who invest in both National Savings Certificates and shares, we can use the concept of sets and intersections.

Let's assume:
- Set A represents the persons who invest in National Savings Certificates.
- Set B represents the persons who invest in shares.

We know that:
- The number of persons who invest in National Savings Certificates (|A|) = 30.
- The number of persons who invest in shares (|B|) = 17.

We need to find the number of persons who invest in both National Savings Certificates and shares (|A ∩ B|).

Using the formula:
|A ∩ B| = |A| + |B| - |A ∪ B|

where |A ∪ B| represents the number of persons who invest in either National Savings Certificates or shares.

Calculating |A ∪ B|:
|A ∪ B| = |A| + |B| - |A ∩ B|
|A ∪ B| = 30 + 17 - |A ∩ B|

We know that the total number of persons = 32. Therefore,
|A ∪ B| = 32

Substituting the values, we get:
32 = 30 + 17 - |A ∩ B|

Simplifying the equation:
32 = 47 - |A ∩ B|
|A ∩ B| = 47 - 32
|A ∩ B| = 15

Therefore, the number of persons who invest in both National Savings Certificates and shares is 15. Hence, the correct option is B) 15.

Answer

n(N ∪ S) = 32, n(N) = 30, n(S) = 17 Since, We know that,
n( N ∪ S) = n(N) + n(S) - n(N ∩ 5)
or 32= 30+ 17 - n(N ∩ S)
or n(N ∩ S ) = 47 - 32= 15
Since, R is an equivalence relation on set A, Therefore, (a, a) ∈ R for all a ∈ A, Hence, R has atleast n ordered pairs.

Answer

n(N ∪ S) = 32, n(N) = 30, n(S) = 17 Since, We know that,
n( N ∪ S) = n(N) + n(S) - n(N ∩ 5)
or 32= 30+ 17 - n(N ∩ S)
or n(N ∩ S ) = 47 - 32= 15
Since, R is an equivalence relation on set A, Therefore, (a, a) ∈ R for all a ∈ A, Hence, R has atleast n ordered pairs.

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