Same chapter3 marksDifficulty: Medium
Is the relation R = {(1, 1), (2, 2), (1, 2)} on the set {1, 2} reflexive, symmetric and transitive?
Relations and Functions
3 marksDifficulty: Medium
What is an equivalence relation? State the three properties it must satisfy.
Original Khojo Papers practice question — not from a past board paper.
Answer
An equivalence relation on a set is a relation that is reflexive, so every element is related to itself; symmetric, so if a is related to b then b is related to a; and transitive, so if a is related to b and b to c then a is related to c.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
An equivalence relation partitions the set into disjoint equivalence classes.
Related questions
From the same topic and chapter, at a similar level.
Same chapter3 marksDifficulty: Medium
What is a binary operation on a set? State when it is commutative and when it is associative.
Relations and Functions
Same chapter3 marksDifficulty: Medium
Define a one-one function, an onto function and a bijection.
Relations and Functions
Same chapter3 marksDifficulty: Medium
If f(x) = 2x + 3 and g(x) = (x − 3)/2, show that g is the inverse of f.
Relations and Functions
Same subject3 marksDifficulty: Medium
If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], find AB and BA and state whether they are equal.
Matrices
Same subject3 marksDifficulty: Medium
Find the projection of a = 2i + 3j + 2k on b = i + 2j + k.
Vectors