If A has 3 elements, how many irreflexive relations can be defined on A?
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Answer and explanation
Correct answer: 2^6
A relation on a three-element set can use 3×3=9 ordered pairs. For an irreflexive relation, the three diagonal pairs (a,a) are forbidden, leaving 9−3=6 off-diagonal pairs. Each of these six pairs may independently be included or excluded, giving 2^6 possible relations. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
2^6
Why is this the correct answer?
A relation on a three-element set can use 3×3=9 ordered pairs. For an irreflexive relation, the three diagonal pairs (a,a) are forbidden, leaving 9−3=6 off-diagonal pairs. Each of these six pairs may independently be included or excluded, giving 2^6 possible relations. Thus option B is correct.
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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