Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function

Solution:

A function that shows both one - one and onto behaviour is called as bijective function.

According to the given problem:

f : A × B → B × A is defined as (a, b) = (b, a).

(a₁, b₁),(a₂, b₂) ∈ A x B such that

f (a₁, b₁) = f (a₂, b₂)

⇒ (b₁, a₁) = (b₂, a₂)

⇒ b₁ = b₂ and a₁ = a₂

⇒ (a₁, b₁) = (a₂, b₂)

⇒ f is one-one.

(b, a) ∈ B × A there exists (a, b) ∈ A × B such that

f (a, b) = & (b, a)

⇒ f is onto.

f is bijective

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.2 Question 8

Let A and B be sets. Show that f : A × B → B × A such that f(a, b) = (b, a) is bijective function.

Summary:

f : A × B → B × A such that f(a, b) = (b, a) is a bijective function as it shows both one to one and onto behavior