Question

If A = {1, 2, 3} and B = {1, 4, 6, 9} and R is a relation from A to B defined by ‘x’ is greater than ‘y’. The range of R is
1). {1, 4, 6, 9}
2). {4, 6, 9}
3). {1}
4). None of these

Answer 1

According to the question, we have to determine the range of R. Relation R from A to B is defined as R = {(x, y): x is greater than y}. x is domain and y is range.
Domain: The domain of a function is the complete set of possible values of the independent variable. Domain in this question is x and its value will be taken from A.
Range: The range of a function is a complete set of all possible resulting values of a dependent variable. Range in this question is y and its values will be taken from B.

Complete step-by-step solution:
Given: x is greater than y
R \subseteq A \times B = \left\\{ {\left( {a,b} \right)a \in A,b \in B} \right\\}
Now, we will write the relation as R = \left\\{ {\left( {x,y} \right):x > y} \right\\}
According to the condition (x is greater than y) given in question we have to find the values to put in the above set to determine the relation. Values of x will be from set A and values of y will be from set B.
If we take 1 from set A there is not any number in set B which is less than 1 so, we can’t take 1. If we take 2 there is a number in set B which is less than 2 and that is 1 so we get (2,1). Similarly, we get (3,1).
R = \left\\{ {\left( {2,1} \right),\left( {3,1} \right)} \right\\}
Now, the range in elements is {1}.
So, option (3) is the correct answer.

Note: Relation is to be made very carefully using the conditions in the question. A relation between two sets is a collection of ordered pairs containing one object from each set. If the object x is from the first set and the object y is from the second set, then the objects are said to be related if the ordered pair (x, y) is in the relation.