# 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).

(a_{1}, b_{1}),(a_{2}, b_{2}) ∈ A x B such that

f (a_{1}, b_{1}) = f (a_{2}, b_{2})

⇒ (b_{1}, a_{1}) = (b_{2}, a_{2})

⇒ b_{1} = b_{2} and a_{1} = a_{2}

⇒ (a_{1}, b_{1}) = (a_{2}, b_{2})

⇒ 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

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

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