Let I = {x ∈ ℕ : x is a multiple of 4 and x < 30}, where ℕ = {1, 2, 3, ...}. How many elements does I have?
Answer and explanation
Correct answer: 7
The positive multiples of 4 that are less than 30 are 4, 8, 12, 16, 20, 24, and 28. The next multiple, 32, is not less than 30, so it must not be included. Therefore, the set is I = {4, 8, 12, 16, 20, 24, 28}, which contains 7 distinct elements. Hence, the cardinality of I is 7, so option B is correct. Specifying positive natural numbers avoids the convention-related issue of whether 0 is included in ℕ.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The positive multiples of 4 that are less than 30 are 4, 8, 12, 16, 20, 24, and 28. The next multiple, 32, is not less than 30, so it must not be included. Therefore, the set is I = {4, 8, 12, 16, 20, 24, 28}, which contains 7 distinct elements. Hence, the cardinality of I is 7, so option B is correct. Specifying positive natural numbers avoids the convention-related issue of whether 0 is included in ℕ.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
