How many reflexive relations on A contain this…

How many reflexive relations on A contain this four-pair R?

Question 44

HardOriginal question

On $A = \{1, 2, 3\}$ , the relation $R = \{(1, 1), (2, 2), (3, 3), (2, 3)\}$ .

How many reflexive relations on $A$ contain this four-pair $R$ ?

16

Correct answerYour answer

32

Correct answerYour answer

64

Correct answerYour answer

512

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

All 4 pairs of $R$ are fixed in; the other $9 - 4 = 5$ pairs of $A \times A$ are free.
$2^{5} = 32$ .

Worth noting

$2^{6}$ counts the reflexive relations with no pair required besides the diagonal.

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

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