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ACT Exam  >  ACT Questions  >  Comprehension:Read the following information ... Start Learning for Free
Comprehension:
Read the following information and answer the questions given below:
A has 28 elements, B has 32 elements and (A U B) has 40 elements.
How many elements are present only in B?
  • a)
    28
  • b)
    18
  • c)
    12
  • d)
    10
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Comprehension:Read the following information and answer the questions ...
Formula used:
n(A U B) = n(A) + n(B) - n(A ∩ B)
n(A) = Number of elements in A, n(B) = Number of elements in B
n(A U B) = Each element in both the set A and set B
n(A ∩ B) = The intersection contains the elements that the two sets have in common.
Calculation:
n(A) = 28
n(B) = 32
n(A U B) = 40
n(A ∩ B) = 32 + 28 - 40 = 20
Elements are present only in B = n(B) - n(A ∩ B) = 32 - 20 = 12
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Comprehension:Read the following information and answer the questions ...
Given:
- Set A has 28 elements.
- Set B has 32 elements.
- The union of sets A and B, denoted as A U B, has 40 elements.

To find:
- The number of elements present only in set B.

Solution:

Step 1: Find the number of elements in the intersection of sets A and B.
- The intersection of sets A and B, denoted as A ∩ B, represents the common elements between the two sets.
- We can find the number of elements in the intersection using the formula: |A ∩ B| = |A| + |B| - |A U B|.
- Substituting the given values, we have: |A ∩ B| = 28 + 32 - 40 = 60 - 40 = 20.

Step 2: Find the number of elements present only in set B.
- The elements present only in set B can be obtained by subtracting the number of elements in the intersection from the total number of elements in set B.
- Using the formula: |B - A| = |B| - |A ∩ B|.
- Substituting the given values, we have: |B - A| = 32 - 20 = 12.

Answer:
- The number of elements present only in set B is 12.
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Community Answer
Comprehension:Read the following information and answer the questions ...
Formula used:
n(A U B) = n(A) + n(B) - n(A ∩ B)
n(A) = Number of elements in A, n(B) = Number of elements in B
n(A U B) = Each element in both the set A and set B
n(A ∩ B) = The intersection contains the elements that the two sets have in common.
Calculation:
n(A) = 28
n(B) = 32
n(A U B) = 40
n(A ∩ B) = 32 + 28 - 40 = 20
Elements are present only in B = n(B) - n(A ∩ B) = 32 - 20 = 12
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Comprehension:Read the following information and answer the questions given below:A has 28 elements, B has 32 elements and (A U B) has 40 elements.How many elements are present only in B?a)28b)18c)12d)10Correct answer is option 'C'. Can you explain this answer?
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