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If A = P {1, 2} where P denotes the power set, then which one of the following is correct?
- a){1,2} ⊂ A
- b)1 ε A
- c)φ ∉ A
- d){1,2} ε A
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If A = P {1, 2} where P denotes the power set, then which one of the f...
A = P {1 ,2} = {φ, {1}, {2}, {1 ,2 }}
From above, it is clear that {1 , 2} ε A
From above, it is clear that {1 , 2} ε A
Most Upvoted Answer
If A = P {1, 2} where P denotes the power set, then which one of the f...
Understanding the Power Set
The power set P{1, 2} includes all possible subsets of the set {1, 2}. Let's first enumerate the elements of this power set:
- The subsets of {1, 2} are:
- The empty set: {}
- The set containing just the first element: {1}
- The set containing just the second element: {2}
- The set containing both elements: {1, 2}
Thus, the power set P{1, 2} is:
P{1, 2} = { {}, {1}, {2}, {1, 2} }
This is the set A.
Analyzing the Options
Now, let's evaluate each of the provided options:
- Option a: {1, 2} ⊆ A
- This is incorrect because {1, 2} is not a subset of A; rather, it is an element of A.
- Option b: 1 ∈ A
- This is also incorrect. The number 1 is not an element of A; the elements of A are sets, not individual numbers.
- Option c: ∅ ∉ A
- This statement is incorrect as well. The empty set ∅ is indeed an element of A.
- Option d: {1, 2} ∈ A
- This is correct. The set {1, 2} is one of the elements in the power set P{1, 2}.
Conclusion
Thus, the correct answer is option 'D': {1, 2} ∈ A. The confusion often arises when distinguishing between elements and subsets within the context of power sets.
The power set P{1, 2} includes all possible subsets of the set {1, 2}. Let's first enumerate the elements of this power set:
- The subsets of {1, 2} are:
- The empty set: {}
- The set containing just the first element: {1}
- The set containing just the second element: {2}
- The set containing both elements: {1, 2}
Thus, the power set P{1, 2} is:
P{1, 2} = { {}, {1}, {2}, {1, 2} }
This is the set A.
Analyzing the Options
Now, let's evaluate each of the provided options:
- Option a: {1, 2} ⊆ A
- This is incorrect because {1, 2} is not a subset of A; rather, it is an element of A.
- Option b: 1 ∈ A
- This is also incorrect. The number 1 is not an element of A; the elements of A are sets, not individual numbers.
- Option c: ∅ ∉ A
- This statement is incorrect as well. The empty set ∅ is indeed an element of A.
- Option d: {1, 2} ∈ A
- This is correct. The set {1, 2} is one of the elements in the power set P{1, 2}.
Conclusion
Thus, the correct answer is option 'D': {1, 2} ∈ A. The confusion often arises when distinguishing between elements and subsets within the context of power sets.
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Community Answer
If A = P {1, 2} where P denotes the power set, then which one of the f...
A = P {1 ,2} = {φ, {1}, {2}, {1 ,2 }}
From above, it is clear that {1 , 2} ε A
From above, it is clear that {1 , 2} ε A
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If A = P {1, 2} where P denotes the power set, then which one of the following is correct?a){1,2} ⊂Ab)1 ε Ac)φ ∉ Ad){1,2} ε ACorrect answer is option 'D'. Can you explain this answer?
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If A = P {1, 2} where P denotes the power set, then which one of the following is correct?a){1,2} ⊂Ab)1 ε Ac)φ ∉ Ad){1,2} ε ACorrect answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about If A = P {1, 2} where P denotes the power set, then which one of the following is correct?a){1,2} ⊂Ab)1 ε Ac)φ ∉ Ad){1,2} ε ACorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A = P {1, 2} where P denotes the power set, then which one of the following is correct?a){1,2} ⊂Ab)1 ε Ac)φ ∉ Ad){1,2} ε ACorrect answer is option 'D'. Can you explain this answer?.
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