Exercise · ZW-BINARY-RELATION-006 · ★★☆ Intermediate
Let \(A=\{1,2,3\}\). How many distinct relations are there from \(A\) to \(A\)?
Choose one option.
Show answer
- D. 512
Explanation
\(A\times A\) has \(3\cdot 3=9\) pairs, and each relation is a subset of it. There are \(2^9=512\) subsets. The value 9 counts pairs, not relations.
Review the concept: Binary relation
A set of ordered pairs \((a,b)\) specifying which elements of \(A\) are related to which elements of \(B\).
\[R \subseteq A \times B\]
More practice problems: binary relation
- ZW-BINARY-RELATION-001 What is a binary relation from A to B?
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- ZW-BINARY-RELATION-003 If R=\(1,2),(2,3)\, what is the domain of R?
- ZW-BINARY-RELATION-004 If R=\(1,2),(2,3)\, what is the range of R?
- ZW-BINARY-RELATION-005 What is the usual notation for saying that a is related to b by R?
- ZW-BINARY-RELATION-007 Let A=\1,2,3\ and R=\(a,b)∈ A× A : a≤ b\. Which of these pairs is in A× A but not in R?
- ZW-BINARY-RELATION-008 Let R=\(a,b)∈ ℕ×ℕ : b=a+1\. Which of these pairs belongs to R?
- ZW-BINARY-RELATION-009 A relation R on A is reflexive if (a,a)∈ R for every a∈ A. With A=\1,2,3\, how many reflexive relat…