If T = {x : x ∈ N, x is a two-digit number and the sum of its digits is 9}, what is the roster form of T?
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Answer and explanation
Correct answer: T = {18, 27, 36, 45, 54, 63, 72, 81, 90}
Let the tens digit range from 1 through 9. For a digit sum of 9, the corresponding units digits are 8, 7, 6, 5, 4, 3, 2, 1, and 0. This gives 18, 27, 36, 45, 54, 63, 72, 81, and 90. The number 9 is not two-digit, so it is excluded, while 90 is included because 9 + 0 = 9.
Frequently asked questions
What is the correct answer to this question?
T = {18, 27, 36, 45, 54, 63, 72, 81, 90}
Why is this the correct answer?
Let the tens digit range from 1 through 9. For a digit sum of 9, the corresponding units digits are 8, 7, 6, 5, 4, 3, 2, 1, and 0. This gives 18, 27, 36, 45, 54, 63, 72, 81, and 90. The number 9 is not two-digit, so it is excluded, while 90 is included because 9 + 0 = 9.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
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