For a five-element set A, how many symmetric relations on A contain no diagonal ordered pair (a,a)?
Answer and explanation
Correct answer: 2^10
A symmetric relation is chosen by deciding independently about each unordered pair. Because diagonal pairs are forbidden, only unordered pairs of distinct elements can be selected. For five elements, their number is 5C2=10. Each pair is either included together with its reverse or omitted, so the total number is 2^10. The larger powers incorrectly include diagonal or duplicate directional choices.
Frequently asked questions
What is the correct answer to this question?
2^10
Why is this the correct answer?
A symmetric relation is chosen by deciding independently about each unordered pair. Because diagonal pairs are forbidden, only unordered pairs of distinct elements can be selected. For five elements, their number is 5C2=10. Each pair is either included together with its reverse or omitted, so the total number is 2^10. The larger powers incorrectly include diagonal or duplicate directional choices.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
