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Relations and Functions

Short Answer Type

51.

Determine the domain and range of the relation defined as :

$space space space space space space space space space space space straight R space equals space left curly bracket left parenthesis straight x comma space straight y right parenthesis space colon space straight x element of straight N comma space straight y element of straight N comma space straight x less than 5 comma space straight y space equals space 3 straight x space plus space 1 right curly bracket$

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52.

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by aRb = {(a, b) : a, $straight b element of straight A$ , a divide b}. determine its domain and range.

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53. Let A = {2, 3, 4, 5}, which of the following relations from A into A is a function? If it is a function, determine the domain and range.

(i) {(2, 3), (2, 4), (2, 5)} (ii) {(2, 2), (3, 3), (4, 5), (5, 3)}

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54.

Let A = {2, 3, 4, 5}, which of the following relations from A into A is a function ? If it is a function, determine the domain and range.

(a) {(2,2), (3, 2), (4,2), (5,2)} (b) {(2, 3), (3,4),(4,5),(3,5)}

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55.
Let A = {2, 3, 4, 5}, which of the following relations from A into A is a function ? If it is a function, determine the domain and range.

{(2, 3), (2, 4), (2, 5)}

(2, 3), (2, 4), (2, 5)

x =2 $space space space element of$ A has more than one image i.e. f(x) = 3, 4, 5

Hence, the set does not represent a function.