Relations Quiz - CBSE Class 11 Mathematics

Free practice quiz: Relations (CBSE Class 11 Mathematics). 14 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 11 Mathematics practice quiz has 14 multiple-choice questions on Relations, and 14 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. Which of the following is an example of a reflexive relation on set A = {1, 2}?

   1. {(1, 1), (2, 2)}
   2. {(1, 2)}
   3. {(2, 1)}
   4. {}
   Show answer

   Answer: A. {(1, 1), (2, 2)}

   A reflexive relation on a set contains all pairs (a, a) for each element a in the set. Since A = {1, 2}, a reflexive relation must include (1, 1) and (2, 2).

2. What is the Cartesian product A x B if A = {1, 2} and B = {x, y}?

   1. {(1, x), (2, y)}
   2. {(1, x), (1, y), (2, x), (2, y)}
   3. {(x, y)}
   4. {1, 2, x, y}
   Show answer

   Answer: B. {(1, x), (1, y), (2, x), (2, y)}

   The Cartesian product A x B is the set of all combinations (a, b) where a is in A and b is in B.

3. Identify the property: If (a, b) ∈ R implies that (b, a) ∈ R for all a, b.

   1. Reflexive
   2. Symmetric
   3. Transitive
   4. Anti-symmetric
   Show answer

   Answer: B. Symmetric

   Symmetric relation criteria are satisfied when if (a, b) ∈ R then (b, a) ∈ R.

4. Which property does an anti-symmetric relation have if (a, b) ∈ R and (b, a) ∈ R?

   1. a = b
   2. a ≠ b
   3. a & b exist
   4. R is reflexive
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   Answer: A. a = b

   An anti-symmetric relation means that if (a, b) and (b, a) are both present in R, then a must equal b.

5. Which among the following relations is not necessarily anti-symmetric?

   1. ≥ on real numbers
   2. Subset relation on sets
   3. Divisor relation on integers
   4. Equality relation on any set
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   Answer: C. Divisor relation on integers

   A divisor relation such as 4|2 and 2|4, does not imply 2 = 4, breaking anti-symmetry.

More questions in this quiz

Answers and explanations are in the full quiz.

1. Determine if the relation R = {(1, 1), (2, 2), (3, 2)} on set A = {1, 2, 3} is reflexive.
2. How many ordered pairs are there in the relation from A = {1, 2} to B = {a, b, c}?
3. Which statement is true about symmetric relations?
4. Which of the following is NOT true for the equivalence relation?
5. If a relation is symmetric and transitive, is it necessarily reflexive?
6. If R and S are equivalence relations on a set A, is their union R ∪ S necessarily an equivalence relation?
7. For a set with 4 elements, how many possible relations could there be?
8. For R = {(a, b), (b, c)}, find conditions under which R is transitive.
9. In a relation R on set A with n elements, if R is universal, what can be said about its properties?

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