Which of these is the universal relation on $A = \{1, 2\}$ ?

\{(1, 1), (2, 2)\}

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\{(1, 2), (2, 1)\}

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\{(1, 1), (1, 2), (2, 1), (2, 2)\}

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\varnothing

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The universal relation relates every element to every element: it is all of $A \times A$ .
$A \times A$ has $2 \times 2 = 4$ pairs.

Worth noting

$\{(1, 1), (2, 2)\}$ is the identity relation, which relates each element only to itself.

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

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

Which of these is the universal relation on A={1,2}A = \{1, 2\}A={1,2}?