Chapter 1 · Mathematics
Empty and Universal Relations
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In a boys' school, who is whose sister? Nobody, and Maths has a name for that. What a relation is, and its two extreme cases.
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Key points
- A relation R in a set A is a subset of A × A.
- Empty relation: no element is related to any element, so R is the empty set.
- Universal relation: every element is related to every element, so R = A × A.
- Both are called trivial relations.
- Every other relation lies between the two.
NCERT's examples
| Set A: students of a boys' school | R | Type |
|---|---|---|
| a is a sister of b | empty set | Empty |
| difference between heights is less than 3 metres | A × A | Universal |
Try it yourself
Goal: See which ordered pairs a rule selects, and when the relation is empty or universal.
- Choose a rule and see which pairs light up.
- Read whether R is empty, universal or in between.
- Tap cells to build your own relation.
- Try to make R empty, then universal.
Quick quiz
3 questions. Choose an answer for each, then submit to see your score and the explanations.
