If  A is a finite set having n elements, then the number of relations which can be defined in A is 

  1. 2n
  2. n2
  3. nn

Answer (Detailed Solution Below)

Option 3 :
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
150 Qs. 600 Marks 150 Mins

Detailed Solution

Download Solution PDF

Calculation:

Set A has n elements.

Relation is simply A × A

So, we can select first element of ordered pair in n ways and second element in n ways.

So, clearly this set of ordered pairs contain n × n = n2 pairs.

Now, each of these n2 ordered pairs can be present in the relation or can't be. So, there are 2 possibilities for each of the n2 ordered pairs.

Thus, the total no. of relations = 2 × 2 × 2 × ......× (n2  times) 

Hence, option (3) is correct.

Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Hot Links: teen patti all game teen patti 50 bonus teen patti king teen patti joy apk