KCET · Maths · Sets and Relations
Let \(A=\{a, b, c\}\), then the number of equivalence relations on \(A\) containing \((b, c)\) is
- A \(1\)
- B \(3\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned}
A & =\{\mathrm{a}, \mathrm{~b}, \mathrm{c}\} \\
\mathrm{R} & =\{(\mathrm{b}, \mathrm{c}),(\mathrm{a}, \mathrm{a}),(\mathrm{b}, \mathrm{~b}),(\mathrm{c}, \mathrm{c}),(\mathrm{c}, \mathrm{~b})\} \\
\mathrm{R} & =\{(\mathrm{a}, \mathrm{a})(\mathrm{b}, \mathrm{~b})(\mathrm{c}, \mathrm{c})(\mathrm{a}, \mathrm{~b})(\mathrm{b}, \mathrm{a})(\mathrm{a}, \mathrm{c})(\mathrm{c}, \mathrm{a})(\mathrm{b}, \mathrm{c})(\mathrm{c}, \mathrm{~b})\}
\end{aligned}\)
Total (2) equivalence relations possible
A & =\{\mathrm{a}, \mathrm{~b}, \mathrm{c}\} \\
\mathrm{R} & =\{(\mathrm{b}, \mathrm{c}),(\mathrm{a}, \mathrm{a}),(\mathrm{b}, \mathrm{~b}),(\mathrm{c}, \mathrm{c}),(\mathrm{c}, \mathrm{~b})\} \\
\mathrm{R} & =\{(\mathrm{a}, \mathrm{a})(\mathrm{b}, \mathrm{~b})(\mathrm{c}, \mathrm{c})(\mathrm{a}, \mathrm{~b})(\mathrm{b}, \mathrm{a})(\mathrm{a}, \mathrm{c})(\mathrm{c}, \mathrm{a})(\mathrm{b}, \mathrm{c})(\mathrm{c}, \mathrm{~b})\}
\end{aligned}\)
Total (2) equivalence relations possible
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(y = \sqrt[3]{\tan x + y}\), then \(\dfrac{dy}{dx} = \)KCET 2026 Easy
- In the interval \((0, \pi / 2)\) area lying between the curves \(y=\tan x\) and \(y=\cot x\) and the \(X\)-axis isKCET 2023 Medium
- If \( 1+\sin \theta+\sin ^{2} \theta+\ldots . \) upto \( \infty=2 \sqrt{3}+4 \), then \( \theta= \)KCET 2016 Medium
- If a line makes angles \(90^{\circ}, 60^{\circ}\) and \(\theta\) with \(\mathrm{x}, \mathrm{y}\) and z axes respectively, where \(\theta\) is acute, then the value of \(\theta\) isKCET 2025 Easy
- The remainder obtained when \(5^{124}\) is divided by 124 isKCET 2007 Medium
- If \(y=\sin x \cdot \sin 2 x \cdot \sin 3 x \ldots \sin n x\), then \(y^{\prime}\) isKCET 2011 Medium
More PYQs from KCET
- For the reaction, \( 2 \mathrm{SO}_{2}+\mathrm{O}_{2} \rightleftharpoons 2 \mathrm{SO}_{3} \), the rate of disappearance of \( \mathrm{O}_{2} \) is
\( 2 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1} \). The rate of apperance of \( \mathrm{SO}_{3} \) isKCET 2018 Easy - The Set A has \( 4 \) elements and the Set B has \( 5 \) elements then the number of injective mappings
that can be defined from A to B isKCET 2016 Medium - If the function \( g(x) \) is defined by
\[
g(x)=\frac{\chi^{200}}{200}+\frac{\chi^{199}}{199}+\frac{\chi^{198}}{198}+\ldots \ldots+\frac{\chi^{2}}{2}+\chi+5, \text { then } g^{\prime}(0)=
\]KCET 2015 Easy - Arrange benzene, \(n\)-hexane and ethyne in decreasing order of their acidic behaviour.KCET 2021 Medium
- Two fixed charges A and B of \(5 \mu \mathrm{C}\) each are separated by a distance of \(6 \mathrm{~m}\). \(\mathrm{C}\) is the mid point of the line joining \(A\) and \(B\). A charge \(Q\) of \(-5 \mu \mathrm{C}\) is shot perpendicular to the line joining A and \(B\) through \(C\) with a kinetic energy of \(0.06 \mathrm{~J}\). The charge \(\mathrm{Q}\) comes to rest at a point D. The distance \(C D\) isKCET 2012 Hard
- Vitellogenesis occurs during the formation ofKCET 2009 Medium