Register

TIFR CSE 2010 | Part A | Question: 15

• edited by
1,511 views
10 votes
10 votes

Let $A, B$ be sets. Let $\bar{A}$ denote the complement of set $A$ (with respect to some fixed universe), and $( A - B)$ denote the set of elements in $A$ which are not in $B$. Set $(A - (A - B))$ is equal to:

  1. $B$
  2. $A\cap \bar{B}$
  3. $A - B$
  4. $A\cap B$
  5. $\bar{B}$
• edited by
User Avatar

3 Answers

Best answer
15 votes
15 votes
$(A - (A - B)) = A ∩ (A ∩ B')'  $  Since $A-B=A∩B'$

                  $=$ $A ∩ (A' U B) $     Since $(A∩B)'$ = $A'UB'  $

                  $=$ $A ∩ B$ Option $D$
• edited by
User Avatar
1 votes
1 votes

(A - (A - B)) = A - (AB') = A(AB')'  = A(A'+B) = AB = A∩B

Option (D) A∩B , is the correct answer.

• edited by
User Avatar
Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

40 votes
40 votes
5 answers
1
makhdoom ghaya asked Oct 4, 2015
4,666 views
TIFR CSE 2010 | Part A | Question: 18
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ? $2^{n+1}$ $2^{2n}$ $3^{n}$ $2^{n} + 1$ $3^{n + 1}$
Let $X$ be a set of size $n$. How many pairs of sets (A, B) are there that satisfy the condition $A\subseteq B \subseteq X$ ?$2^{n+1}$$2^{2n}$$3^{n}$$2^{n} + 1$$3^{n + 1}...
User Avatar
13 votes
13 votes
2 answers
4
makhdoom ghaya asked Oct 4, 2015
1,781 views
TIFR CSE 2010 | Part A | Question: 20
How many integers from $1$ to $1000$ are divisible by $30$ but not by $16$? $29$ $31$ $32$ $33$ $25$
How many integers from $1$ to $1000$ are divisible by $30$ but not by $16$?$29$$31$$32$$33$$25$
User Avatar
Link Copied!