CA Foundation Exam > CA Foundation Questions > If A = {3, 4, 5, 6} B = {3, 7, 9, 5} and C = ...
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If A = {3, 4, 5, 6} B = {3, 7, 9, 5} and C = {6, 8, 10, 12, 7} then (A∪B')' is (given that the universal set U = {3, 4, ...., 11, 12, 13}
- a){3, 4, 5, 6}
- b){3, 7, 9, 5}
- c){8, 10, 11, 12, 13}
- d)None
Correct answer is option 'C'. Can you explain this answer?
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If A = {3, 4, 5, 6} B = {3, 7, 9, 5} and C = {6, 8, 10, 12, 7} then (A...
Understanding the Problem
To solve the problem, we need to find the union of sets A and B, and then see what that set is in relation to the universal set U.
Given Sets
- Set A = {3, 4, 5, 6}
- Set B = {3, 7, 9, 5}
- Universal Set U = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
Finding the Union of A and B
- The union of two sets combines all unique elements from both sets.
- A ∪ B = {3, 4, 5, 6} ∪ {3, 7, 9, 5}
- Combine the elements: {3, 4, 5, 6, 7, 9}
Result of the Union
- So, A ∪ B = {3, 4, 5, 6, 7, 9}
Comparing with the Options
Now, we need to check which of the provided options does not belong to the union:
- Option a: {3, 4, 5, 6} - This is a subset of A.
- Option b: {3, 7, 9, 5} - This is a subset of A ∪ B.
- Option c: {8, 10, 11, 12, 13} - None of these elements are in A ∪ B.
- Option d: None - This is not applicable.
Conclusion
The correct answer is option 'C' since {8, 10, 11, 12, 13} contains only elements not found in A ∪ B. Hence, it is accurate to say that option C is the correct answer.
To solve the problem, we need to find the union of sets A and B, and then see what that set is in relation to the universal set U.
Given Sets
- Set A = {3, 4, 5, 6}
- Set B = {3, 7, 9, 5}
- Universal Set U = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
Finding the Union of A and B
- The union of two sets combines all unique elements from both sets.
- A ∪ B = {3, 4, 5, 6} ∪ {3, 7, 9, 5}
- Combine the elements: {3, 4, 5, 6, 7, 9}
Result of the Union
- So, A ∪ B = {3, 4, 5, 6, 7, 9}
Comparing with the Options
Now, we need to check which of the provided options does not belong to the union:
- Option a: {3, 4, 5, 6} - This is a subset of A.
- Option b: {3, 7, 9, 5} - This is a subset of A ∪ B.
- Option c: {8, 10, 11, 12, 13} - None of these elements are in A ∪ B.
- Option d: None - This is not applicable.
Conclusion
The correct answer is option 'C' since {8, 10, 11, 12, 13} contains only elements not found in A ∪ B. Hence, it is accurate to say that option C is the correct answer.
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If A = {3, 4, 5, 6} B = {3, 7, 9, 5} and C = {6, 8, 10, 12, 7} then (A∪B) is (given that the universal set U = {3, 4, ...., 11, 12, 13}a){3, 4, 5, 6}b){3, 7, 9, 5}c){8, 10, 11, 12, 13}d)NoneCorrect answer is option 'C'. Can you explain this answer?
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