If f: A →B is a bijection, then (a) n(A)=n(B) (b) n(A)>n(B) (c) n(A)<n(B) (d) n(A)=n(b)+1

Name: Problem 81, Chapter 1: IIT JEE Super Course in Mathematics: Calculus
Uploaded: 2021-06-08T10:15:28-08:00
Duration: 2 min 10 s
Channel: Goutam Chand
Description: If f: A →B is a bijection, then (a) n(A)=n(B) (b) n(A)>n(B) (c) n(A)<n(B) (d) n(A)=n(b)+1

step 1 In this question it is told that if a function is defined from set A to B and it is a bijective

Question

If $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is a bijection, then (a) $\mathrm{n}(\mathrm{A})=\mathrm{n}(\mathrm{B})$ (b) $\mathrm{n}(\mathrm{A})>\mathrm{n}(\mathrm{B})$ (c) $\mathrm{n}(\mathrm{A})<\mathrm{n}(\mathrm{B})$ (d) $\mathrm{n}(\mathrm{A})=\mathrm{n}(\mathrm{b})+1$

   If $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is a bijection, then
(a) $\mathrm{n}(\mathrm{A})=\mathrm{n}(\mathrm{B})$
(b) $\mathrm{n}(\mathrm{A})>\mathrm{n}(\mathrm{B})$
(c) $\mathrm{n}(\mathrm{A})<\mathrm{n}(\mathrm{B})$
(d) $\mathrm{n}(\mathrm{A})=\mathrm{n}(\mathrm{b})+1$

IIT JEE Super Course in Mathematics: Calculus

Trishna Knowledge… 1st Edition

Chapter 1, Problem 81

Instant Answer

Solved by Expert Goutam Chand

06/08/2021

Step 1

In this case, we cannot create a one-to-one mapping from A to B, because there will be elements in A that do not have a corresponding element in B. This means the function is not bijective. Show more…

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If $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is a bijection, then (a) $\mathrm{n}(\mathrm{A})=\mathrm{n}(\mathrm{B})$ (b) $\mathrm{n}(\mathrm{A})>\mathrm{n}(\mathrm{B})$ (c) $\mathrm{n}(\mathrm{A})<\mathrm{n}(\mathrm{B})$ (d) $\mathrm{n}(\mathrm{A})=\mathrm{n}(\mathrm{b})+1$

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Key Concepts

Bijection

A bijection is a type of function where every element in one set (the domain) is paired with a unique element in another set (the codomain), and every element in the codomain is paired with exactly one unique element in the domain. This ensures that there is a one-to-one correspondence between the two sets, which is fundamental in understanding how the sets relate in terms of size.

Cardinality

Cardinality refers to the number of elements in a set. In the context of functions, if there exists a bijection between two sets, it implies that the sets have the same number of elements. This concept is widely used in mathematics to compare the sizes of both finite and infinite sets.

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