| 1. \[A\cup B\] and \[B\cup D\] are always disjoint. |
| 2. \[A\cap C\] and \[B\cap D\] are always disjoint. |
| Which of the above statements is/are correct? |
A) 1 Only
B) 2 only
C) Both 1 and 2
D) neither 1 nor 2s
Correct Answer: B
Solution :
| [b]Let \[A=\{1,2\}\] |
| \[B=\{3,4,0\}\] |
| \[C=\{5,6,0\}\] |
| \[D=\{7,8\}\] |
| Such that \[(A\cap B)=(C\cap D)=\phi \] |
| \[\Rightarrow (A\cup C)=\{1,2,5,6,0\}\] |
| \[\Rightarrow (B\cup D)=\{3,4,7,8,0\}\] |
| \[\Rightarrow (A\cup C)\cap (B\cup D)=\{0\}\] |
| So \[(A\cup C)\] and \[(B\cup D)\] are not always disjoint |
| \[\Rightarrow (A\cap C)=\phi \] and \[(B\cap D)=\phi \] |
| So \[(A\cap C)\] and \[(B\cap D)\]are always disjoint. |
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