If U1={1,2,3,4,5}, U2={1,2,3,4,5,6,7}, and A={2,5}, which extra elements are in A^c relative to U2 compared with A^c relative to U1?
Advertisement
Answer and explanation
Correct answer: {6,7}
The complement depends on the universal set. Relative to U1, A^c=U1−A={1,3,4}. Relative to U2, the complement is A^c=U2−A={1,3,4,6,7}. Comparing these two complements, the elements that appear only in the second one are 6 and 7. Thus the extra elements are {6,7}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
{6,7}
Why is this the correct answer?
The complement depends on the universal set. Relative to U1, A^c=U1−A={1,3,4}. Relative to U2, the complement is A^c=U2−A={1,3,4,6,7}. Comparing these two complements, the elements that appear only in the second one are 6 and 7. Thus the extra elements are {6,7}, making option A correct.
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.
Advertisement