If U = {1, 2, 3, 4, 5, 6, 7, 8} and A = {1, 4, 6, 8}, how many elements of A' are less than 5?
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Answer and explanation
Correct answer: 2
The complement is formed relative to U: A' = U \ A = {2, 3, 5, 7}. Now apply the strict condition “less than 5.” The elements 2 and 3 satisfy it, while 5 does not because it is equal to 5. Therefore, exactly two elements of A' are less than 5. This also shows why counting 5 would produce the incorrect answer 3.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The complement is formed relative to U: A' = U \ A = {2, 3, 5, 7}. Now apply the strict condition “less than 5.” The elements 2 and 3 satisfy it, while 5 does not because it is equal to 5. Therefore, exactly two elements of A' are less than 5. This also shows why counting 5 would produce the incorrect answer 3.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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