Question

Determine if the given two sets are equal; equivalent; both (equal and equivalent); or none of these. A={x∣x is a letter in the word smile } and B={x∣x is a letter in the word while }

Answer 1

Sets A and B are equivalent because they both contain five elements, but they are not equal because they do not have the exact same elements.

Step-by-step explanation:

To determine if the given two sets A and B are equal, equivalent, both, or neither, let us first list the elements of each set. Set A consists of the letters in the word smile, so A = {s, m, i, l, e}. Set B consists of the letters in the word while, so B = {w, h, i, l, e}. Comparing the two sets:

• Equal sets have exactly the same elements. A and B are not equal because A contains 's' and 'm' that are not in B, and B contains 'w' and 'h' that are not in A.
• Equivalent sets have the same number of elements. Both A and B have five elements each, therefore, they are equivalent.

Thus, the sets A and B are equivalent but not equal.