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Mathematics, 13.03.2020 01:02 krog79
For each of the following determine whether the relation on the given set is reflexive, symmetric, transitive, and an equivalence relation (where ⇐⇒ means if and only if). Justify each of your answers (with proof or counterexamples).
1. R={(f, g)|f(1)=g(1)}on the set A={f|f:Z→Z}
2. R={(f, g)|f(0)=g(0)or f(1)=g(1)}on set A={f|f:Z→Z}
3. ((a, b),(c, d))∈R⇐⇒a+d=b+c on A=Z×Z
4. xRy⇐⇒x−y ∈ Z on A=R
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For each of the following determine whether the relation on the given set is reflexive, symmetric, t...
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