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If A is the set of whole numbers and B i...

If A is the set of whole numbers and B is the set of natural numbers, then `(A-B)` is __________ set.
(singleton/null)

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The correct Answer is:
To solve the question, we need to determine what the set \( A - B \) represents, where \( A \) is the set of whole numbers and \( B \) is the set of natural numbers. ### Step-by-step Solution: 1. **Define the Sets**: - The set of whole numbers \( A \) is defined as: \[ A = \{0, 1, 2, 3, 4, \ldots\} \] - The set of natural numbers \( B \) is defined as: \[ B = \{1, 2, 3, 4, \ldots\} \] 2. **Understand the Operation \( A - B \)**: - The operation \( A - B \) means we take all the elements in set \( A \) and remove all the elements that are also in set \( B \). 3. **Perform the Set Difference**: - Start with set \( A \): \[ A = \{0, 1, 2, 3, 4, \ldots\} \] - Remove elements of set \( B \) from set \( A \): - Remove \( 1 \): \( A \) becomes \( \{0, 2, 3, 4, \ldots\} \) - Remove \( 2 \): \( A \) becomes \( \{0, 3, 4, \ldots\} \) - Remove \( 3 \): \( A \) becomes \( \{0, 4, \ldots\} \) - Continue this process for all natural numbers. - The only element that remains in \( A \) after removing all elements of \( B \) is \( 0 \). 4. **Identify the Resulting Set**: - After performing the set difference, we have: \[ A - B = \{0\} \] 5. **Classify the Resulting Set**: - The set \( \{0\} \) contains exactly one element. Therefore, it is classified as a **singleton set**. ### Final Answer: Thus, \( (A - B) \) is a **singleton set**. ---
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PEARSON IIT JEE FOUNDATION-SETS-TEST YOUR CONCEPTS (Very Short Answer Type Questions)
  1. If X-Y=Y-X, the X and Y are sets. (equal/equivalent)

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  2. In the above Venn diagram n,(ADeltaB)= .

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  3. If A is the set of whole numbers and B is the set of natural numbers, ...

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  4. If A={1,2,3,4}, then the number of subsets of A are .

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  5. (Auuvarphi^(c))^(c)=

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  6. If A nn mu = mu and B uu phi = phi, then A uu B = "".

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  7. If A = {1,8,6,3,7,0} and B = {3,8,1,6,7}, then A -B =

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  8. If A and B are non-empty sets, A nn B = B and A uu B = B, then A and ...

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  9. If n(A xx B) = 15, then the maximum possiblity of n(B) is 3. (True/Fal...

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  10. If A is any non-empty set, with 3 elements then number of subsets of A...

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  11. If X={S,T,U,V} and Y = {s,t,u,v}, then P and Q are sets. (equal/equiv...

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  12. If PsubeQ and QsubeP, then .

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  13. If A and B are two non-empty sets, then n(A xxB) can be 17. (True/Fal...

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  14. If A and B are disjoint sets, then draw their venn diagram

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  15. If A and B are two non-empty sets and A - B is a null set, then "".

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  16. If n (A Delta B) = 12 and n(A nn B) = 3, then find the greatest possib...

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  17. If A = {1,2}, B = {1,2,3} and c = {1,2,3,4,5} then the relation betwee...

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  18. If B is contained in A and C is contained in B, then relation between ...

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  19. If A={1,2,3,4,5, 6} and B = {4,1}, then find (AuuB)-(AnnB).

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  20. If (2x+3,4y-3) = (9,13) then find x + y.

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