What is an equivalence relation? State the three properties it must satisfy.
Relations and Functions
Original Khojo Papers practice question — not from a past board paper.
It is reflexive and transitive but not symmetric.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Both (1,1) and (2,2) are present so it is reflexive; (1,2) is present but (2,1) is not, so it is not symmetric; no pair violates transitivity.
From the same topic and chapter, at a similar level.
What is an equivalence relation? State the three properties it must satisfy.
Relations and Functions
What is a binary operation on a set? State when it is commutative and when it is associative.
Relations and Functions
Define a one-one function, an onto function and a bijection.
Relations and Functions
If f(x) = 2x + 3 and g(x) = (x − 3)/2, show that g is the inverse of f.
Relations and Functions
If A = [[1, 2], [3, 4]] and B = [[0, 1], [1, 0]], find AB and BA and state whether they are equal.
Matrices
Find the projection of a = 2i + 3j + 2k on b = i + 2j + k.
Vectors