How many relations that are both reflexive and symmetric are there on a set with 4 elements?

16

Correct answerYour answer

64

Correct answerYour answer

1{,}024

Correct answerYour answer

4{,}096

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

The 4 diagonal pairs are fixed; the off-diagonal pairs come in $\frac{16 - 4}{2} = 6$ blocks $\{(a, b), (b, a)\}$ .
$2^{6} = 64$ .

Worth noting

$2^{12}$ counts the reflexive relations; symmetry then ties the off-diagonal pairs into blocks.

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

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

Explanation