1.

Determine the domain and range of the following relations : S = {a, b): b = |a-1|, a Z and |a| ≤ 3}

Answer»

Given,

S = {a, b) : b = |a-1|, a Z and |a| ≤ 3} 

Z denotes integer which can be positive as well as negative 

Now, 

|a| ≤ 3 and b = |a-1| 

∴ a {-3, -2, -1, 0, 1, 2, 3} 

S = {a, b): b = |a-1|, a Z and |a| ≤ 3} 

⇒ S = {a, |a-1|): b = |a-1|, a Z and |a| ≤ 3} 

⇒ S = {(-3, |-3 – 1|), (-2, |-2 – 1|), (-1, |-1 – 1|), (0, |0 – 1|), (1, |1 – 1|), (2, |2 – 1|), (3, |3 – 1|)} 

⇒ S = {(-3, |-4|), (-2, |-3|), (-1, |-2|), (0, |-1|), (1, |0|), (2, |1|), (3, |2|)} 

⇒ S = {(-3, 4), (-2, 3), (-1, 2), (0, 1), (1, 0), (2, 1), (3, 2)} 

So, 

Domain of relation S = {-3, -2, -1, 0, 1, 2, 3} 

Range of relation S = {0, 1, 2, 3, 4}


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