Exercise 272Logic, sets and proofs › RelationsHigh schoolAdded 3 Nov 2026

Binary relations

#binary relation#definition#examples

Statement

Let $A=\{1,2,3,4\}$ . Define the relation $\mathcal{R}$ on $A$ by $a\mathcal{R}b\iff a\le b$ . List all elements of $\mathcal{R}$ as a set of ordered pairs.

Hint

$\mathcal{R}\subseteq A\times A$ consists of all pairs $(a,b)$ with $a\le b$ .

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Solution

List.
$\mathcal{R}=\{(1,1),(1,2),(1,3),(1,4),(2,2),(2,3),(2,4),(3,3),(3,4),(4,4)\}.$

Count. $10$ pairs.

Conclusion. The relation $\le$ on $A$ is the set of $10$ ordered pairs above.

Binary relations

Statement

Solution

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