Let |A|=5. A relation R on A is reflexive and symmetric and is required to contain (1,2). How many such relations are possible?
Answer and explanation
Correct answer: 2^9
Reflexivity fixes all five diagonal pairs in R. Symmetry groups the ten unordered pairs of distinct elements into ten independent choices. Since (1,2) is required, one of those ten choices is fixed as included; its reverse (2,1) is then also fixed. The remaining nine unordered pairs may independently be included or omitted, giving 2^9 possibilities.
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What is the correct answer to this question?
2^9
Why is this the correct answer?
Reflexivity fixes all five diagonal pairs in R. Symmetry groups the ten unordered pairs of distinct elements into ten independent choices. Since (1,2) is required, one of those ten choices is fixed as included; its reverse (2,1) is then also fixed. The remaining nine unordered pairs may independently be included or omitted, giving 2^9 possibilities.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
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