KCET · Maths · Sets and Relations
Let \(R\) be an equivalence relation defined on a set containing 6 elements. The minimum number or ordered pairs that \(R\) should contain is
- A 12
- B 6
- C 64
- D 36
Answer & Solution
Correct Answer
(B) 6
Step-by-step Solution
Detailed explanation
Given that,
\(\mathrm{R} \rightarrow\) equivalence relation on a set \(\mathrm{A}\)
Let \(\mathrm{A}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}\}\)
Since, \(R\) is an equivalence relation on set \(A\), then it must be satisfies reflexive property, for this.
\[
\mathrm{aRa}, \forall \mathrm{a} \in \mathrm{A}
\]
That mean minimum number of elements in ' \(R\) ' should be six
\(e g, \quad \mathrm{R}=\{(\mathrm{a}, \mathrm{a}),(\mathrm{b}, \mathrm{b}),(\mathrm{c}, \mathrm{c}),(\mathrm{d}, \mathrm{d})\)
\((e, e),(f, f)\}\)
\(\mathrm{R} \rightarrow\) equivalence relation on a set \(\mathrm{A}\)
Let \(\mathrm{A}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}, \mathrm{e}, \mathrm{f}\}\)
Since, \(R\) is an equivalence relation on set \(A\), then it must be satisfies reflexive property, for this.
\[
\mathrm{aRa}, \forall \mathrm{a} \in \mathrm{A}
\]
That mean minimum number of elements in ' \(R\) ' should be six
\(e g, \quad \mathrm{R}=\{(\mathrm{a}, \mathrm{a}),(\mathrm{b}, \mathrm{b}),(\mathrm{c}, \mathrm{c}),(\mathrm{d}, \mathrm{d})\)
\((e, e),(f, f)\}\)
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
- The value of \(\sin \frac{5 \pi}{12} \sin \frac{\pi}{12}\) isKCET 2022 Easy
- \( \int \frac{\sin ^{2} x}{1+\cos x} d x \)KCET 2015 Easy
- A unit vector perpendicular to the plane containing the vectors \( \hat{i}+2 \hat{j}+\hat{k} \) and
\( -2 \hat{i}+\hat{j}+3 \hat{k} \) isKCET 2019 Hard - Probability of at least one of the events A and B occur is \(0.6\). If A and B occur simultaneously with probability \(0.2\), then \(P(\bar{A}) + P(\bar{B})\) isKCET 2026 Easy
- The maximum value of \( \left(\frac{1}{x}\right)^{x} \) isKCET 2016 Hard
- \(A\) and \(B\) are non-singleton sets and \(n(A \times B)=35\). If \(B \subset A\), then \({ }^{n(A)} C_{n(B)}\) is equal toKCET 2021 Easy
More PYQs from KCET
- If \( \left|\begin{array}{ccc}2 a & x_{1} & y_{1} \\ 2 b & x_{2} & y_{2} \\ 2 c & x_{3} & y_{3}\end{array}\right|=\frac{a b c}{2} \neq 0 \), then the area of the triangle whose vertices are
\[
\left(\frac{x_{1}}{a}, \frac{y_{1}}{a}\right),\left(\frac{x_{2}}{b}, \frac{y_{2}}{b}\right),\left(\frac{x_{3}}{c}, \frac{y_{3}}{c}\right) \text { is }
\]KCET 2015 Easy - A transformer works on the principle ofKCET 2011 Easy
- dsRNA is used to develop pest resistant tobacco plant by a technique called.KCET 2018 Hard
- Which of the following aqueous solutions should have the highest boiling point?KCET 2018 Medium
- The oxide of potassium that does not exist isKCET 2020 Easy
- Excess of carbon dioxide is passed through 50 \(\mathrm{mL}\) of \(0.5 \mathrm{M}\) calcium hydroxide solution. After the completion of the reaction, the solution was evaporated to dryness. The solid calcium carbonate was completely neutralised with \(0.1 \mathrm{~N}\) hydrochloric acid. The volume of hydrochloric acid required is (Atomic mass of calcium \(=40\) )KCET 2009 Hard