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Which of the following is NOT a valid set? a. {1,2,3,4} b. {apple, banana, cherry} c. {{1},{2},{3}} d. {5,6,5}

Question

Which of the following is NOT a valid set?

a. {1,2,3,4}
b. {apple, banana, cherry}
c. {{1},{2},{3}}
d. {5,6,5}

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Solution

To determine which of the given options is NOT a valid set, we need to recall the definition of a set in mathematics:

A set is a collection of distinct objects, meaning that all elements in a set must be unique.

Evaluation of Each Option

  1. Option a: {1,2,3,4}\{1, 2, 3, 4\}

    • All elements are distinct. This is a valid set.

  2. Option b: {apple,banana,cherry}\{apple, banana, cherry\}

    • All elements are distinct. This is a valid set.

  3. Option c: {{1},{2},{3}}\{\{1\}, \{2\}, \{3\}\}

    • All elements are distinct (as sets). This is a valid set.

  4. Option d: {5,6,5}\{5, 6, 5\}

    • Here, the number 55 is repeated. Therefore, it contains non-distinct elements, making it invalid as a set.

Conclusion

Hence, the option that is NOT a valid set is:

Final Answer: d. {5,6,5}\{5, 6, 5\}

This problem has been solved

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