How many elements are in D={x: x∈Z and -3<x≤2}?
Answer and explanation
Correct answer: 5
The governing concept is counting integers in a half-open interval. Since -3<x, the integer -3 is excluded; since x≤2, the endpoint 2 is included. Listing the permitted integers gives -2,-1,0,1,2. There are five distinct values, so the cardinality of D is 5. Therefore option B is correct; counts of 4, 6, or 7 result from mishandling an endpoint or adding an outside integer.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The governing concept is counting integers in a half-open interval. Since -3<x, the integer -3 is excluded; since x≤2, the endpoint 2 is included. Listing the permitted integers gives -2,-1,0,1,2. There are five distinct values, so the cardinality of D is 5. Therefore option B is correct; counts of 4, 6, or 7 result from mishandling an endpoint or adding an outside integer.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Common Questions. Topic: General chapter practice.
