Set Operations
If \(A\) and \(B\) are subsets of \(U=\{1,2,3,4,5\}\) such that \[A \cup B = U, A\cap B =\emptyset, \] how many possible choices are there for the ordered pair \((A,B)\)?
Details and assumptions
It is possible that \(A = \emptyset\) or \(B = \emptyset\).
by
Sandeep Mehra
Let \(A\) and \(B\) be two sets and \(U\) be a universal set such that \(|U|=700\), \(|A|=200\), \(|B|=300\) and \(|A\cap B|=100\). Find \(|A^{C}\cap B^{C}|\).
by
Omkar Kulkarni
Which of the following sequence of set operations counts the number of elements that are in exactly one of \(A\), \(B\) or \(C\)?"
Options:
\(|A\cap B|+|B\cap C|+|C\cap A|-3(|A\cap B\cap C|)\)
\(|A|+|B|+|C|-2(|A\cap B|+|B\cap C|+|C\cap A|)+3|A\cap B\cap C|\)
\(|A\cap B|+|B\cap C|+|C\cap A|-2|A\cap B\cap C|\)
\(|A|+|B|+|C|-|A\cap B|-|B\cap C|-|C\cap A|+|A\cap B\cap C|\)
\(|(A\cap B\cap C)\cup(A\cap B^{C}\cap C^{C})\cup(A^{C}\cap B\cap C^{C})\cup(A^{C}\cap B^{C}\cap C)|\)
|\(A\cup B\cup C\) |
by
Omkar Kulkarni
If X and Y are two sets, X \(∩\) \((Y∪X)^c\) is equal to
Details and assumptions:
\(\rightarrow\) \(∩\) represents intersection.
\(\rightarrow\) \(∪\) represents union.
\(\rightarrow\) \(X^c\) represents compliment of set X.
by
Akhil Bansal
In what percentage of cases are they likely to contradict each other in stating the same fact?
by
Sandeep Bhardwaj