If V₁ = {x : x is a number from 1 to 30 whose sum of digits is 5}, what is V₁?
Answer and explanation
Correct answer: V₁ = {5, 14, 23}
We examine every number from 1 through 30 and select those whose digits add to 5. The number 5 has digit sum 5, 14 has digit sum 1 + 4 = 5, and 23 has digit sum 2 + 3 = 5. The other listed alternatives contain numbers such as 15, 25, 30, or 32, whose digit sums are not 5 or whose values are outside the interval 1 to 30. Hence V₁ = {5, 14, 23}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
V₁ = {5, 14, 23}
Why is this the correct answer?
We examine every number from 1 through 30 and select those whose digits add to 5. The number 5 has digit sum 5, 14 has digit sum 1 + 4 = 5, and 23 has digit sum 2 + 3 = 5. The other listed alternatives contain numbers such as 15, 25, 30, or 32, whose digit sums are not 5 or whose values are outside the interval 1 to 30. Hence V₁ = {5, 14, 23}, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
