• TOC
  • Courses
  • Blog
  • Twitch
  • Shop
  • Search
    • Courses
    • Blog
    • Subreddit
    • Discord
    • Log in
    • Sign up
    • ▾Bridge course
      • •Countable and uncountable sets
      • ▸Proof techniques
        • •Example of a nonconstructive proof
        • •Direct proof
        • •Disproof by counterexample
        • •Proof by cases
        • •Proving properties of absolute value
        • •Proof by contrapositive
        • •Proof by contradiction
        • •Proof by induction
        • •Proof by strong induction
        • •Proving de Moivre's theorem
        • •Visual proof
        • •Challenge
      • ▾Relations
        • •Equivalence relations
        • •Intersection of equivalence relations
        • •Representing relations using matrices
        • ▸Combining relations
          • •Composition of relations
        • •Inverse of composite relation
        • •Representing relations using digraphs
        • •Properties of relations
        • •Proving equivalence relations
        • •What is a relation?
        • •Finding the inverse of a relation on a finite set
      • ▸Functions (bridge course)
        • ▸Injective, surjective, and bijective
          • •Intro
          • •Is it bijective? (infinite domain)
          • •Is it injective?
          • ▸Is it surjective?
            • •Proof: Composite of surjections is surjection
          • •Proving properties of injective, surjective, and bijective functions
     › Bridge course › Relations

    Inverse of composite relation

    Let \(\mathcal{R}_2 \circ \mathcal{R}_1 \subseteq S_1 \times S_3\) be the composite of the two relations \(\mathcal{R}_1 \subseteq S_1 \times S_2\) and \(\mathcal{R}_2 \subseteq S_2 \times S_3\). Then \((\mathcal{R}_2 \circ \mathcal{R}_1)^{-1} = \mathcal{R}_1^{-1} \circ \mathcal{R}_2^{-1}\).
    7921Inverse of Composite Relation
    ProofWiki