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If A = {1, 2, 5, 7} and B = {2, 4, 6} then find the number of proper subsets of A U B ?
- a)127
- b)64
- c)63
- d)31
- e)none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If A = {1, 2, 5, 7} and B = {2, 4, 6} then find the number of proper s...
CALCULATION:
Given: A = {1, 2, 5, 7} and B = {2, 4, 6}
As we know that, A ∪ B = {x : x ∈ A or x ∈ B}.
⇒ A ∪ B = {1, 2, 4, 5, 6, 7}
As we can see that, the number of elements present in A U B = 6 i.e n(A U B) = 6
As we know that, if A is a non-empty set such that n(A) = m then numbers of proper subsets of A is given by 2m - 1.
So, the number of proper subsets of A Δ B = 26 - 1 = 63
Hence, the correct option is 3.
Most Upvoted Answer
If A = {1, 2, 5, 7} and B = {2, 4, 6} then find the number of proper s...
Step 1: Find A U B
To find the union of sets A and B:
- A = {1, 2, 5, 7}
- B = {2, 4, 6}
The union A U B combines all unique elements from both sets:
- A U B = {1, 2, 4, 5, 6, 7}
Step 2: Count the Elements in A U B
Now, we count the number of elements in A U B:
- Number of elements in A U B = 6 (i.e., 1, 2, 4, 5, 6, 7)
Step 3: Calculate Total Subsets of A U B
The formula for the total number of subsets of a set is 2 raised to the power of the number of elements in the set:
- Total subsets = 2^n, where n is the number of elements
Thus, for A U B:
- Total subsets = 2^6 = 64
Step 4: Identify Proper Subsets
A proper subset is any subset that is not equal to the set itself. Therefore, to find the number of proper subsets, we subtract 1 from the total number of subsets:
- Proper subsets = Total subsets - 1 = 64 - 1 = 63
Conclusion
The number of proper subsets of A U B is:
- 63
Thus, the correct answer is option 'C'.
To find the union of sets A and B:
- A = {1, 2, 5, 7}
- B = {2, 4, 6}
The union A U B combines all unique elements from both sets:
- A U B = {1, 2, 4, 5, 6, 7}
Step 2: Count the Elements in A U B
Now, we count the number of elements in A U B:
- Number of elements in A U B = 6 (i.e., 1, 2, 4, 5, 6, 7)
Step 3: Calculate Total Subsets of A U B
The formula for the total number of subsets of a set is 2 raised to the power of the number of elements in the set:
- Total subsets = 2^n, where n is the number of elements
Thus, for A U B:
- Total subsets = 2^6 = 64
Step 4: Identify Proper Subsets
A proper subset is any subset that is not equal to the set itself. Therefore, to find the number of proper subsets, we subtract 1 from the total number of subsets:
- Proper subsets = Total subsets - 1 = 64 - 1 = 63
Conclusion
The number of proper subsets of A U B is:
- 63
Thus, the correct answer is option 'C'.
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If A = {1, 2, 5, 7} and B = {2, 4, 6} then find the number of proper subsets of A U B ?a)127b)64c)63d)31e)none of theseCorrect 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 If A = {1, 2, 5, 7} and B = {2, 4, 6} then find the number of proper subsets of A U B ?a)127b)64c)63d)31e)none of theseCorrect 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 If A = {1, 2, 5, 7} and B = {2, 4, 6} then find the number of proper subsets of A U B ?a)127b)64c)63d)31e)none of theseCorrect answer is option 'C'. Can you explain this answer?.
If A = {1, 2, 5, 7} and B = {2, 4, 6} then find the number of proper subsets of A U B ?a)127b)64c)63d)31e)none of theseCorrect 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 If A = {1, 2, 5, 7} and B = {2, 4, 6} then find the number of proper subsets of A U B ?a)127b)64c)63d)31e)none of theseCorrect 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 If A = {1, 2, 5, 7} and B = {2, 4, 6} then find the number of proper subsets of A U B ?a)127b)64c)63d)31e)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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