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Equal & Equivalent Sets Video Lecture | Mathematics (Maths) Class 11 - Commerce
FAQs on Equal & Equivalent Sets Video Lecture - Mathematics (Maths) Class 11 - Commerce
| 1. What is the difference between equal and equivalent sets? |  |
Ans. Equal sets refer to two sets that have exactly the same elements, while equivalent sets refer to sets that have the same cardinality (number of elements). In other words, equal sets are identical, whereas equivalent sets may not have the same elements but have an equal number of elements.
| 2. Can two equal sets be considered equivalent? | |
Ans. Yes, two equal sets are always considered equivalent. Since equal sets have the same elements, they automatically have the same cardinality, making them equivalent as well.
| 3. Are all equivalent sets also equal? | |
Ans. No, all equivalent sets are not necessarily equal. Equivalent sets can have different elements, but they have the same number of elements. On the other hand, equal sets have the same elements, making them identical.
| 4. What is an example of equal sets that are not equivalent? | |
Ans. An example of equal sets that are not equivalent is {1, 2, 3} and {4, 5, 6}. These sets have the same elements, but they do not have the same number of elements. Hence, they are equal but not equivalent.
| 5. How can we prove that two sets are equivalent? | |
Ans. Two sets can be proven to be equivalent by establishing a one-to-one correspondence between their elements. If a function can be defined that maps each element of one set to a unique element in the other set, and vice versa, then the two sets are considered equivalent.
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