Probability

Set Operations

Set Operations: Level 2 Challenges

         

If AA and BB are subsets of U={1,2,3,4,5}U=\{1,2,3,4,5\} such that AB=U,AB=,A \cup B = U, A\cap B =\emptyset, how many possible choices are there for the ordered pair (A,B)(A,B)?

Details and assumptions

It is possible that A=A = \emptyset or B=B = \emptyset.

Let AA and BB be two sets and UU be a universal set such that U=700|U|=700, A=200|A|=200, B=300|B|=300 and AB=100|A\cap B|=100. Find ACBC|A^{C}\cap B^{C}|.

Which of the following sequence of set operations counts the number of elements that are in exactly one of AA, BB or CC?"

Options:

  1. AB+BC+CA3(ABC)|A\cap B|+|B\cap C|+|C\cap A|-3(|A\cap B\cap C|)

  2. A+B+C2(AB+BC+CA)+3ABC|A|+|B|+|C|-2(|A\cap B|+|B\cap C|+|C\cap A|)+3|A\cap B\cap C|

  3. AB+BC+CA2ABC|A\cap B|+|B\cap C|+|C\cap A|-2|A\cap B\cap C|

  4. A+B+CABBCCA+ABC|A|+|B|+|C|-|A\cap B|-|B\cap C|-|C\cap A|+|A\cap B\cap C|

  5. (ABC)(ABCCC)(ACBCC)(ACBCC)|(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)|

  6. |ABCA\cup B\cup C |

If XX and YY are two sets, X(YX)cX \cap (Y \cup X)^c is equal to

Details and assumptions:
\rightarrow \cap represents intersection.
\rightarrow \cup represents union.
\rightarrow XcX^c represents compliment of set XX.

Person "A" says the truth 60% of the time, and person "B" does so 90% of the time.

In what percentage of cases are they likely to contradict each other in stating the same fact?

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