JEE Exam > JEE Questions > Choose the correct statementa){2} ⊆ {1,4,6}.....
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Choose the correct statement
a){2} ⊆ {1,4,6}
b){2,4,6} ⊂ {2}
c){2} ⊂ {2,4,6}
d){2} ⊇ {2,4,6}
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Choose the correct statementa){2} ⊆ {1,4,6}... moreb){2,4,6} ⊂ {2}c){2...
Understanding Set Notation
In set theory, it's essential to understand the different symbols and their meanings:
- ⊆ means "is a subset of."
- ⊂ means "is a proper subset of" (contains some but not all elements).
- ⊇ means "is a superset of."
Analyzing the Options
Let's break down each option to find out why option 'C' is correct.
Option A: {2} ⊆ {1, 4, 6}
- This statement is false because the set {2} is not a subset of {1, 4, 6}. The elements of {2} do not appear in {1, 4, 6}.
Option B: {2, 4, 6} ⊂ {2}
- This statement is also false. The set {2, 4, 6} cannot be a proper subset of {2} since it contains more elements than {2}.
Option C: {2} ⊂ {2, 4, 6}
- This statement is true. The set {2} is indeed a proper subset of {2, 4, 6} because all elements of {2} are in {2, 4, 6}, and {2, 4, 6} contains additional elements (4 and 6).
Option D: {2} ⊇ {2, 4, 6}
- This statement is false as well. {2} cannot be a superset of {2, 4, 6} because it does not contain all the elements of the latter set.
Conclusion
The correct answer is option 'C' because it accurately describes the relationship between the sets. Understanding subset and superset relationships is crucial in set theory, especially in contexts like JEE.
In set theory, it's essential to understand the different symbols and their meanings:
- ⊆ means "is a subset of."
- ⊂ means "is a proper subset of" (contains some but not all elements).
- ⊇ means "is a superset of."
Analyzing the Options
Let's break down each option to find out why option 'C' is correct.
Option A: {2} ⊆ {1, 4, 6}
- This statement is false because the set {2} is not a subset of {1, 4, 6}. The elements of {2} do not appear in {1, 4, 6}.
Option B: {2, 4, 6} ⊂ {2}
- This statement is also false. The set {2, 4, 6} cannot be a proper subset of {2} since it contains more elements than {2}.
Option C: {2} ⊂ {2, 4, 6}
- This statement is true. The set {2} is indeed a proper subset of {2, 4, 6} because all elements of {2} are in {2, 4, 6}, and {2, 4, 6} contains additional elements (4 and 6).
Option D: {2} ⊇ {2, 4, 6}
- This statement is false as well. {2} cannot be a superset of {2, 4, 6} because it does not contain all the elements of the latter set.
Conclusion
The correct answer is option 'C' because it accurately describes the relationship between the sets. Understanding subset and superset relationships is crucial in set theory, especially in contexts like JEE.
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Community Answer
Choose the correct statementa){2} ⊆ {1,4,6}... moreb){2,4,6} ⊂ {2}c){2...
Yes option C is correct as {2} is a subset of {2, 4, 6}.
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Choose the correct statementa){2} ⊆ {1,4,6}... moreb){2,4,6} ⊂ {2}c){2} ⊂ {2,4,6}d){2} ⊇ {2,4,6}Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Choose the correct statementa){2} ⊆ {1,4,6}... moreb){2,4,6} ⊂ {2}c){2} ⊂ {2,4,6}d){2} ⊇ {2,4,6}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Choose the correct statementa){2} ⊆ {1,4,6}... moreb){2,4,6} ⊂ {2}c){2} ⊂ {2,4,6}d){2} ⊇ {2,4,6}Correct answer is option 'C'. Can you explain this answer?.
Choose the correct statementa){2} ⊆ {1,4,6}... moreb){2,4,6} ⊂ {2}c){2} ⊂ {2,4,6}d){2} ⊇ {2,4,6}Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Choose the correct statementa){2} ⊆ {1,4,6}... moreb){2,4,6} ⊂ {2}c){2} ⊂ {2,4,6}d){2} ⊇ {2,4,6}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Choose the correct statementa){2} ⊆ {1,4,6}... moreb){2,4,6} ⊂ {2}c){2} ⊂ {2,4,6}d){2} ⊇ {2,4,6}Correct answer is option 'C'. Can you explain this answer?.
Solutions for Choose the correct statementa){2} ⊆ {1,4,6}... moreb){2,4,6} ⊂ {2}c){2} ⊂ {2,4,6}d){2} ⊇ {2,4,6}Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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