What is the possible number of reflexive relations on a set of 5 elements?

2018

What is the possible number of reflexive relations on a set of 5 elements?

  1. A.

    210

  2. B.

    215

  3. C.

    220

  4. D.

    225

Attempted by 86 students.

Show answer & explanation

Correct answer: C

$$\text{Total Reflexive Relations} = 2^{(n^2 - n)}$$

Calculation for 5 Elements

Given n = 5:

$$\text{Number of relations} = 2^{(5^2 - 5)}$$

$$\text{Number of relations} = 2^{(25 - 5)}$$

$$\text{Number of relations} = 2^{20}$$

Therefore, the correct choice is 3) 2^20.

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