Let A={1,2,3}. If a symmetric relation R on A must contain (1,2), how many such relations are possible?
Answer and explanation
Correct answer: 32
Since R is symmetric, the presence of (1,2) forces (2,1) to be present as well. The remaining independent choices are the three diagonal pairs (1,1), (2,2), (3,3), and the two unordered off-diagonal pairs represented by (1,3) and (2,3). Thus there are 5 freely selectable pairs, giving 2^5=32 relations. The other options use an incorrect number of independent choices.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
Since R is symmetric, the presence of (1,2) forces (2,1) to be present as well. The remaining independent choices are the three diagonal pairs (1,1), (2,2), (3,3), and the two unordered off-diagonal pairs represented by (1,3) and (2,3). Thus there are 5 freely selectable pairs, giving 2^5=32 relations. The other options use an incorrect number of independent choices.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Introduction to Relations.
