Questions: Determine whether the following pair of sets is equivalent. Justify your answer. 5,10,15,20 and a, e, i, o

Determine whether the following pair of sets is equivalent. Justify your answer. 5,10,15,20 and a, e, i, o
Transcript text: 8. Determine whether the following pair of sets is equivalent. Justify your answer. \[ \{5,10,15,20\} \text { and }\{a, e, i, \text { o }\} \]
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Solution

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Solution Steps

Step 1: Understand the concept of equivalent sets

Two sets are considered equivalent if there exists a one-to-one correspondence (bijection) between their elements. This means that the sets must have the same number of elements.

Step 2: Count the number of elements in each set
  • The first set \( \{5, 10, 15, 20\} \) has 4 elements.
  • The second set \( \{a, e, i, o\} \) also has 4 elements.
Step 3: Compare the number of elements

Since both sets have the same number of elements (4), a one-to-one correspondence can be established between them. Therefore, the sets are equivalent.

Final Answer

The sets are equivalent: \( \boxed{\text{Yes}} \)

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