Answer to Question #261542 in Discrete Mathematics for Amraj

Question

2. Equal sets are always equivalent but equivalent sets may not be equal. Justify

Answer 1

Solution:

Yes, all equal sets are also equivalent sets. Equal sets have the exact same elements, so they must have the same number of elements. Therefore, equal sets must also be equivalent. No, not all equivalent sets are also equal sets.

Two sets are said to be equal if they contain exactly the same elements (no matter the order, since sets are not ordered. So, for example,

A={1,2,3},B={2,1,3} are two equal set.

On the other hand, two sets are said to be equivalent if they have the same amount of elements. So, for example, all the sets containing only two elements are equivalent:

A={1,2},B={π,ϕ},C={car,cat} are all equivalent.