If P₁ = {x : x ∈ ℤ, x² < 10}, how many elements are in P₁?
Answer and explanation
Correct answer: 7
The condition x² < 10 is satisfied by the integers whose absolute value is less than √10, approximately 3.16. Therefore the possible integers are −3, −2, −1, 0, 1, 2, and 3. The numbers −4 and 4 are excluded because their squares are 16. Counting the listed values gives 7 elements, so P₁ is a finite set with cardinality 7.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The condition x² < 10 is satisfied by the integers whose absolute value is less than √10, approximately 3.16. Therefore the possible integers are −3, −2, −1, 0, 1, 2, and 3. The numbers −4 and 4 are excluded because their squares are 16. Counting the listed values gives 7 elements, so P₁ is a finite set with cardinality 7.
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.
