Exercise · ZW-BINARY-RELATION-009 · ★★★ Advanced
A relation \(R\) on \(A\) is reflexive if \((a,a)\in R\) for every \(a\in A\). With \(A=\{1,2,3\}\), how many reflexive relations on \(A\) are there?
Choose one option.
Show answer
- A. 64
Explanation
The 3 pairs \((a,a)\) are forced, and the 6 remaining pairs are free: \(2^6=64\). The value 512 counts all relations, without requiring reflexivity.
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?
- ZW-BINARY-RELATION-002 How many pairs does A × B have if |A|=2 and |B|=3?
- 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-006 Let A=\1,2,3\. How many distinct relations are there from A to A?
- 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?