If A has 4 elements, how many irreflexive relations are possible on A?
Answer and explanation
Correct answer: 2^12
A four-element set produces 4^2=16 possible ordered pairs. Irreflexivity excludes the four diagonal pairs (a,a), so only 16−4=12 off-diagonal pairs remain available. Each remaining pair can independently be included or omitted, giving 2^12 relations. Thus option A is correct; 2^16 would count unrestricted relations instead.
Frequently asked questions
What is the correct answer to this question?
2^12
Why is this the correct answer?
A four-element set produces 4^2=16 possible ordered pairs. Irreflexivity excludes the four diagonal pairs (a,a), so only 16−4=12 off-diagonal pairs remain available. Each remaining pair can independently be included or omitted, giving 2^12 relations. Thus option A is correct; 2^16 would count unrestricted relations instead.
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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