If S = {x : x is a two-digit natural number}, what type of set is S?
Answer and explanation
Correct answer: Finite set
Two-digit natural numbers start at 10 and end at 99, so S = {10, 11, 12, ..., 99}. The number of elements is 99 − 10 + 1 = 90. Since the lower and upper bounds are fixed, the list has a limited number of members and is therefore finite. It is not empty because such numbers exist, not infinite because the list stops at 99, and “equal set” does not describe its cardinality.
Frequently asked questions
What is the correct answer to this question?
Finite set
Why is this the correct answer?
Two-digit natural numbers start at 10 and end at 99, so S = {10, 11, 12, ..., 99}. The number of elements is 99 − 10 + 1 = 90. Since the lower and upper bounds are fixed, the list has a limited number of members and is therefore finite. It is not empty because such numbers exist, not infinite because the list stops at 99, and “equal set” does not describe its cardinality.
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.
