Question 1 :
Let A = {1, 2, 3, 4,..., 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A x A. Also, find the domain and range of R.
Solution :
A = {1, 2, 3, 4,..., 45}
Let "A" be a set which contains some of elements of A
A = {1, 2, 3, 4, 5, 6}
Now, we have to write the other set of elements from A. The elements in this set denotes the square value of previous set.
Square values of set A = {1, 4, 9, 16, 25, 36}
A x A = {(1, 1)(1,4)(1, 9)(1, 16) (1, 25) (1, 36)..................}
Domain = {1, 2, 3, 4, 5, 6}
Range = {1, 4, 9, 16, 25, 36}
Question 2 :
A Relation R is given by the set {(x, y) /y = x + 3, x ∈ {0, 1, 2, 3, 4, 5}}. Determine its domain and range.
Solution :
Given that :
y = x + 3
y = x + 3 x = 0 y = 0 + 3 y = 3 |
y = x + 3 x = 1 y = 1 + 3 y = 4 |
y = x + 3 x = 2 y = 2 + 3 y = 5 |
y = x + 3 x = 3 y = 3 + 3 y = 6 |
y = x + 3 x = 4 y = 4 + 3 y = 7 |
y = x + 3 x = 5 y = 5 + 3 y = 8 |
R = {(0, 3) (1, 4) (2, 5) (3, 6) (4, 7) (5, 8)}
Domain of R = {0, 1, 2, 3, 4, 5}
Range of R = {3, 4, 5, 6, 7, 8}
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