How many elements are in the set C = {x : x ∈ ℕ, x² - 7x + 12 = 0}?
Answer and explanation
Correct answer: 2
Factor the equation x² - 7x + 12 = 0 as (x - 3)(x - 4) = 0. Its solutions are x = 3 and x = 4. Both are natural numbers, so both satisfy the defining condition of C. Therefore C = {3, 4}, which contains exactly two distinct elements. Repeated or equivalent descriptions would not increase the cardinality, but here the two roots are distinct.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
Factor the equation x² - 7x + 12 = 0 as (x - 3)(x - 4) = 0. Its solutions are x = 3 and x = 4. Both are natural numbers, so both satisfy the defining condition of C. Therefore C = {3, 4}, which contains exactly two distinct elements. Repeated or equivalent descriptions would not increase the cardinality, but here the two roots are distinct.
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.
