For reflexive (x,x)∈R,x∈Z ⇒x+x=2x→ even For symmetric of (x,y)∈R then (y,x)∈R when x,y∈Z x+y→ even ⇒y+x→ even for transitive if (x,y)∈R⇒x+y→ even (y,z)∈R⇒y+z→ even x+2y+z→ even ⇒x+z is even ⇒(x,z)∈R ⇒R is an equivalence relation.
The relation R={(x,y):x,y∈Z and x+y is even } is:
Held on 28 Jan 2025 · Verified 6 Jul 2026.
reflexive and symmetric but not transitive
an equivalence relation
symmetric and transitive but not reflexive
reflexive and transitive but not symmetric
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