Question:
If A and B are two sets, such that A has 20 elements, \( A \cup B \) has 32 elements, and \( A \cap B \) has 10 elements, the number of elements in the set B is:
If A and B are two sets, such that A has 20 elements, \( A \cup B \) has 32 elements, and \( A \cap B \) has 10 elements, the number of elements in the set B is:
Show Hint
Use the principle of inclusion and exclusion to calculate the size of set B when you know the sizes of \( A \), \( A \cup B \), and \( A \cap B \).
Updated On: Mar 10, 2025
- 22
- 12
- 32
- 42
- 52
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The formula for the union of two sets is:
\[
|A \cup B| = |A| + |B| - |A \cap B|
\]
Substituting the given values:
\[
32 = 20 + |B| - 10
\]
\[
|B| = 22
\]
Was this answer helpful?
0
0
Top Questions on sets
- The modulus of the complex number \( z \) such that \( |z + 3 - i| = 1 \) and \( \arg(z) = \pi \) is equal to:
- If \( a>0, b>0, c>0 \) and \( a, b, c \) are distinct, then \( (a + b)(b + c)(c + a) \) is greater than:
- In a statistical investigation of 1003 families of Calcutta, it was found that 63 families have neither a radio nor a TV, 794 families have a radio, and 187 have a TV. The number of families having both a radio and a TV is:
- Number of subsets of set of letters of word 'MONOTONE' is:
- Let \( X \) and \( Y \) be subsets of \( \mathbb{R} \). If \( f : X \rightarrow Y \) given by \( f(x) = -8(x + 5)^2 \) is one-to-one, then the codomain \( Y \) is:
View More Questions
Questions Asked in KEAM exam
- In the measurement of length 6 $\mu$m is equal to $x$ pm. Then the value of $x$ is
- KEAM - 2024
- Dimensional Analysis
- If the lines \( \frac{x-1}{2} = \frac{y-2}{\alpha} = \frac{z-3}{2} \) and \( \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-3}{-2} \) are perpendicular, then the value of \( \alpha \) is:
- KEAM - 2024
- Integration
- An organic compound contains 37.5% C, 12.5% H and the rest oxygen. What is the empirical formula of the compound?
- KEAM - 2024
- Oxygen
- Let A, B, C denote the set of students in a college who play football, basketball, and cricket respectively. If \( n(A) = 60 \), \( n(B) = 55 \), \( n(C) = 70 \), \( n(A \cup B \cup C) = 100 \) and \( n(A \cap B \cap C) = 20 \), then the number of students who play exactly two of these sports is
- KEAM - 2024
- Relations and functions
For the reaction:
\[ 2A + B \rightarrow 2C + D \]
The following kinetic data were obtained for three different experiments performed at the same temperature:
\[ \begin{array}{|c|c|c|c|} \hline \text{Experiment} & [A]_0 \, (\text{M}) & [B]_0 \, (\text{M}) & \text{Initial rate} \, (\text{M/s}) \\ \hline I & 0.10 & 0.10 & 0.10 \\ II & 0.20 & 0.10 & 0.40 \\ III & 0.20 & 0.20 & 0.40 \\ \hline \end{array} \]
The total order and order in [B] for the reaction are respectively:
- KEAM - 2024
- Grignard’s reagents and their uses
View More Questions