Muft Shiksha
Update

Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है

Subjects
Class 11MathematicsRelations and FunctionsRelationsHardLevel 25
0 reads0 ratings0 helpful

For the empty relation ∅ on A = {1,2,3}, which statement is correct?

Advertisement

Answer and explanation

Correct answer: It is symmetric and transitive but not reflexive

The empty relation contains no ordered pairs. Symmetry is vacuously true because there is no pair (a,b) that could violate the requirement; transitivity is also vacuously true because there are no pairs (a,b) and (b,c) to test. However, reflexivity requires all three diagonal pairs (1,1), (2,2), and (3,3), none of which is present. Thus option A is correct, and the relation cannot be an equivalence relation because reflexivity fails.

Related tags

RelationsEmpty RelationRelation Properties

Frequently asked questions

What is the correct answer to this question?

It is symmetric and transitive but not reflexive

Why is this the correct answer?

The empty relation contains no ordered pairs. Symmetry is vacuously true because there is no pair (a,b) that could violate the requirement; transitivity is also vacuously true because there are no pairs (a,b) and (b,c) to test. However, reflexivity requires all three diagonal pairs (1,1), (2,2), and (3,3), none of which is present. Thus option A is correct, and the relation cannot be an equivalence relation because reflexivity fails.

Which subject and chapter does this question cover?

This is a Class 11 Mathematics question. Chapter: Relations and Functions. Topic: Relations.

Was this question useful?

No ratings yetWrite a review / Rate this question

Student Reviews

No published reviews yet.

KEEP PRACTISING

10 more MCQs
  1. 1Which option correctly shows the limited roster form of N = {x : x is an odd whole number and x < 8}?
  2. 2If \(A=\{1,2,3,4\}\), \(B=\{a,b\}\), and \(R=\{(x,y):x\in A,\ y\in B,\ x\text{ is even}\}\), which of the following ordered pairs belongs to \(R\)?
  3. 3If A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}, and R = {(a, b) : a² < b}, how many ordered pairs are in R, that is, what is |R|?
  4. 4If A={1,2,3,4,5}, B={1,2,3,4,5}, and R={(a,b): a+b=7}, which of the following ordered pairs must belong to R⁻¹?
  5. 5If \(A=\{1,2,3,4,5\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b):a+b\le6\}\), how many ordered pairs in \(R\) have an even first component \(a\)?
  6. 6If A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5, 6}, and R = {(a, b) ∈ A × B : b = 2a or b = 3a}, what is the value of |R|?
  7. 7If \(A=\{0,1,2,3,4\}\), \(B=\{0,1,2,3,4\}\), and \(R=\{(a,b)\in A\times B: a^2\equiv b\pmod{5}\}\), what is the value of \(|R|\)?
  8. 8If \(A=\{1,2,3,4\}\), \(B=\{1,2,3,4,5\}\), and \(R=\{(a,b): b-a\in\{0,2\}\}\), where \(a\in A\) and \(b\in B\), what is the value of \(|R|\)?
  9. 9If (A={1,2}) and (B={3,4}), then a relation from (A) to (B) is a subset of what?
  10. 10If A = {a, b} and B = {1}, how many ordered pairs are in A × B?
Advertisement