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Subjects
Class 11MathematicsRelations and FunctionsRelationsHardLevel 25
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If A has 4 elements, how many reflexive relations are possible on A?

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Answer and explanation

Correct answer: 2^12

A relation on a four-element set is a subset of A×A, which contains 4×4 = 16 ordered pairs. Reflexivity requires all four diagonal pairs (a,a) to be present. The remaining 16−4 = 12 off-diagonal pairs may each be included or excluded independently. Therefore the number of reflexive relations is 2^12, making option A correct. Option B counts arbitrary relations, whereas options C and D do not account for the independent choices among all remaining pairs.

Related tags

RelationsReflexive RelationsCounting

Frequently asked questions

What is the correct answer to this question?

2^12

Why is this the correct answer?

A relation on a four-element set is a subset of A×A, which contains 4×4 = 16 ordered pairs. Reflexivity requires all four diagonal pairs (a,a) to be present. The remaining 16−4 = 12 off-diagonal pairs may each be included or excluded independently. Therefore the number of reflexive relations is 2^12, making option A correct. Option B counts arbitrary relations, whereas options C and D do not account for the independent choices among all remaining pairs.

Which subject and chapter does this question cover?

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

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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?
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