On A={1,2}, how many relations are not reflexive?
Answer and explanation
Correct answer: 12
Option C is correct. A set with two elements has 2×2=4 possible ordered pairs, so it has 2^4=16 total relations. For a relation to be reflexive, both diagonal pairs (1,1) and (2,2) must be included; the other two pairs may be chosen freely, giving 2^2=4 reflexive relations. Therefore, the number that are not reflexive is 16−4=12.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Option C is correct. A set with two elements has 2×2=4 possible ordered pairs, so it has 2^4=16 total relations. For a relation to be reflexive, both diagonal pairs (1,1) and (2,2) must be included; the other two pairs may be chosen freely, giving 2^2=4 reflexive relations. Therefore, the number that are not reflexive is 16−4=12.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Reflexive relation.
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