Question:
Let \( D = \{a, b, c\} \). How many distinct ways can \( D \) be partitioned into non-empty subsets, representing equivalence relations?
Let \( D = \{a, b, c\} \). How many distinct ways can \( D \) be partitioned into non-empty subsets, representing equivalence relations?
Show Hint
For finding distinct partitions of a set, you can use the Bell number or directly list the partitions for small sets.
Updated On: Mar 19, 2026
- 2
- 3
- 5
- 6
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The number of distinct partitions of a set \( D \) into non-empty subsets is equal to the number of equivalence relations on \( D \).
For \( D = \{a, b, c\} \), the number of distinct partitions is 3.
This corresponds to the partitions \( \{\{a\}, \{b, c\}\} \), \( \{\{a, b\}, \{c\}\} \), and \( \{\{a, b, c\}\} \).
Was this answer helpful?
0
0
Top JEE Main Mathematics Questions
- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
- If , then the general value of is:
- The general solution of
- If the constant term in the binomial expansion of $\left(\frac{x^{\frac{3}{2}}}{2}-\frac{4}{x^l}\right)^9$ is $-84$ and the coefficient of $x^{-3 l}$ is $2^\alpha \beta$, where $\beta<0$ is an odd number, then $|\alpha l-\beta|$ is equal to_____
View More Questions
Top JEE Main Miscellaneous Questions
- A bag contains 4 red balls, 3 blue balls, and 2 green balls. Two balls are picked at random. What is the probability that both balls are of the same color?
- A circle passes through the points \( (1, 1) \) and \( (2, -1) \), and its center lies on the line \( x + y = 4 \). What is the radius of the circle?
- If |A| = 2, B = adj(adj(2A)), A is a 3×3 matrix, and tr(A) = 3, what is tr(B) + |B|?
- From the English alphabets, 5 letters are chosen and arranged in alphabetical order. The total number of ways in which the middle letter is M is:
- Which of the following does not belong to the same group?
View More Questions
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
View More Questions