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ZWMath›Set theory›Relations and functions›Binary relation›ZW-BINARY-RELATION-008
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AreaFoundationsCourseSet theoryTopicRelations and functions
Operations and families6
  • Set membership
  • Union of families
  • Intersection of families
  • Relative complement
  • Power set
  • Subset Modern algebra I
Relations and functions9
  • Binary relation
  • Equivalence relation
  • Equivalence class
  • Injective function
  • Surjective function
  • Bijective function
  • Image and preimage
  • Composition and inverse
  • Cartesian product Modern algebra I
Cardinals7
  • Finite set
  • Infinite set
  • Equipotence
  • Countable set
  • Cantor's diagonal theorem
  • Cardinal number
  • Schröder–Bernstein theorem
Ordinals and axioms8
  • Well-ordering
  • Transfinite induction
  • Axiom of choice
  • Zorn's lemma
  • Zermelo–Fraenkel axioms
  • Construction of the naturals
  • Construction of the reals
  • Partial order relation Discrete mathematics

Exercise · ZW-BINARY-RELATION-008 · ★★☆ Intermediate

Let \(R=\{(a,b)\in \mathbb{N}\times\mathbb{N} : b=a+1\}\). Which of these pairs belongs to \(R\)?

Choose one option.

Show answer
  • B. \((4,5)\)

← Back to the question

Explanation

For \((4,5)\) we have \(5=4+1\). The other pairs do not satisfy \(b=a+1\).

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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-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…

← ZW-BINARY-RELATION-007 ZW-BINARY-RELATION-009 →

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