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

To solve the given question, let's break it down step by step.

We are given:

A = {1, 2, 3}
B = {1, 4, 6, 9}
The relation R is defined by "x is greater than y" where x ∈ A and y ∈ B.
The question asks for the range of the relation R.

Understanding the Relation:
A relation R from set A to set B means that we will check for pairs (x, y) such that x ∈ A and y ∈ B. According to the given relation "x is greater than y", for each element x in set A, we will see if it satisfies x > y for any y in set B.

Step-by-step analysis:
For x = 1 (from A):

1 > 1? No
1 > 4? No
1 > 6? No
1 > 9? No Thus, no pairs where x = 1 satisfy the relation.
For x = 2 (from A):

2 > 1? Yes
2 > 4? No
2 > 6? No
2 > 9? No Thus, the pair (2, 1) satisfies the relation.
For x = 3 (from A):

3 > 1? Yes
3 > 4? No
3 > 6? No
3 > 9? No Thus, the pair (3, 1) satisfies the relation.
Range of the Relation:
The range of the relation refers to all the values of y (from set B) that are related to at least one x in set A. From our analysis, the pairs satisfying "x > y" are:

(2, 1)
(3, 1)
From these pairs, the only value of y that appears is 1.

Thus, the range of the relation R is {1}.

Final Answer:
The correct answer is 3) {1}.