Verifying properties of relations

Task number: 3368

Determine which of the following relations are reflexive, symmetric, transitive or antisymmetric.

  • Variant

    \(X=\{a,b,c\}\), \(R=\{(a,a),(a,b),(b,b),(b,a),(c,c)\}\)

  • Variant

    \(X=\{a,b,c\}\), \(R=\{(a,a),(c,c)\}\)

  • Variant

    \((X,R)=(\mathbb N,\leq)\),

  • Variant

    \(X=\{1{,}2,…,10\}\), \(R=\{(x,y): gcd(x,y)=1\}\), i.e. \(x\) and \(y\) are relatively prime.

Difficulty level: Easy task (using definitions and simple reasoning)
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