JEE Exam > JEE Notes > Sets and Functions > Practice Exercise: Subsets
Practice Exercise: Subsets | Sets and Functions - JEE PDF Download
-> Make correct statements by filling in the symbols ⊂ or ⊄ in the blank spaces :
1. {x : x is a student of Class XI of your school}. . .{x : x student of your school}
2. {x : x is an equilateral triangle in a plane} . . . {x : x is a triangle in the same plane}
3. {x : x is an even natural number} . . . {x : x is an integer}
4. φ . . . { 1, 3 }, where φ is an empty set.
-> Let A = { 1, 2, { 3, 4 }, 5 }. Which of the following statements are incorrect and why?
Note that φ is an empty set.
(i) {3, 4} ⊂ A
(ii) {3, 4} ∈ A
(iii) {{3, 4}} ⊂ A
(iv) 1 ∈ A
(v) 1 ⊂ A
(vi) {1, 2, 5} ⊂ A
(vii) {1, 2, 5} ∈ A
(viii) {1, 2, 3} ⊂ A
(ix) φ ∈ A
(x) φ ⊂ A
(xi) {φ} ⊂ A
The document Practice Exercise: Subsets | Sets and Functions - JEE is a part of the JEE Course Sets and Functions.
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FAQs on Practice Exercise: Subsets - Sets and Functions - JEE
| 1. What is the concept of subsets in JEE? |  |
Ans. In JEE (Joint Entrance Examination), the concept of subsets refers to a set that contains elements of another set. It is a fundamental concept in mathematics and is extensively used in various topics of JEE, such as permutations, combinations, and probability.
| 2. How do subsets relate to the JEE exam? | |
Ans. Subsets are an important topic in the JEE exam as they form the basis of many concepts and problem-solving techniques. Questions related to subsets can be asked in various sections of the JEE exam, including mathematics and logic-based questions.
| 3. What are the properties of subsets in JEE? | |
Ans. Subsets in JEE have several properties that are essential to understand. Some of these properties include:
- Every set is a subset of itself.
- The empty set is a subset of every set.
- If A is a subset of B and B is a subset of A, then A and B are equal sets.
- If A is a subset of B and B is a subset of C, then A is a subset of C.
| 4. How can I determine the number of subsets of a set in JEE? | |
Ans. To determine the number of subsets of a set in JEE, we can use the concept of power set. The power set of a set with 'n' elements will have 2^n subsets. For example, if a set has 3 elements, its power set will have 2^3 = 8 subsets.
| 5. Can you provide an example of a JEE-level question involving subsets? | |
Ans. Sure! Here's an example of a JEE-level question involving subsets:
Question: Let A = {1, 2, 3}. How many non-empty subsets of A have the property that the sum of their elements is an even number?
Answer: The subsets that have the sum of their elements as an even number will have either all odd elements or all even elements. Since A has 3 elements, there are 2^3 = 8 subsets in total. Out of these, there are 2^2 - 1 = 3 subsets with all odd elements (excluding the empty set), and 2^1 - 1 = 1 subset with all even elements (excluding the empty set). Therefore, the total number of non-empty subsets of A with the sum of their elements as an even number is 3 + 1 = 4.
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