How many reflexive relations can be defined on a set with 4 elements?

16

Correct answerYour answer

1{,}024

Correct answerYour answer

4{,}096

Correct answerYour answer

65{,}536

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The 4 pairs $(a, a)$ are fixed; each of the other $16 - 4 = 12$ pairs is in or out.
$2^{12} = 4096$ .

Worth noting

$2^{16}$ counts every relation, reflexive or not.

Ten questions from Relations & Functions, at your own pace.

Ten questions from Relations & Functions, at your own pace.

Explanation