Question

If R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 5} is a relation in z, then domain of R is

Answer 1

Answer:

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Step-by-step explanation:

We have R={(x,y):x,y∈Z,x

2

+y

2

≤4}.

Let x=0∴x

2

+y

2

≤4⇒y

2

≤4⇒y=0,±1,±2

Let x=±1∴x

2

+y

2

≤4⇒y

2

≤3⇒y=0,±1

Let x=±2∴x

2

+y

2

≤4⇒y

2

≤0⇒y=0

∴R={(0,0),(0,−1),(0,1),(0,−2),(0,2),(−1,0),(1,0),(1,1),(1,−1),(−1,1),(2,0),(−2,0)}

∴ Domain of R={x:(x,y)ϵR}={0,−1,1,−2,2}.