Is the relation R = {(1, 1), (2, 2), (1, 2)} on the set {1, 2} reflexive, symmetric and transitive?
Relations and Functions
Original Khojo Papers practice question — not from a past board paper.
A function is one-one, or injective, if distinct elements of the domain have distinct images. It is onto, or surjective, if every element of the co-domain is the image of at least one element of the domain. A function that is both one-one and onto is a bijection.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Only a bijection has an inverse function.
From the same topic and chapter, at a similar level.
Is the relation R = {(1, 1), (2, 2), (1, 2)} on the set {1, 2} reflexive, symmetric and transitive?
Relations and Functions
What is a binary operation on a set? State when it is commutative and when it is associative.
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
What is an equivalence relation? State the three properties it must satisfy.
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