Equivalence Relations and Equivalence Classes

Chapter 1 Relations and Functions Class 12 Maths

A relation R on set A is said to be reflexive if (a, a) ∈ R, ∀ a ∈ A or aRa,∀a ∈ A symmetric if(a, b) ∈ R ⇒ (b, a) ∈ R, ∀ a, b ∈ A or aRb ⇒ bRa,∀ a, b ∈ A transitive if (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R, ∀ a, b, c ∈ A or aRb and bRc ⇒ aRc ,  ∀ a, b, c ∈ A If a relation is reflexive, symmetric and transitive then the relation is said to be equivalence relation.

check-if-a-function-is-one-one-and-onto 09:10

Check if a function is one-one and onto

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November 1, 2022, 5:14 am

Question. Let A = R – {3} and B = R – {1}. Consider the function {\displaystyle f: A \rightarrow B } defined by {\displaystyle f(x) = \frac{x-2}{x-3} } . Is f one-one and onto? Justify your answer.