Probability

Set Operations

Sets - Operations on Multiple sets

         

Consider a ground set UU and let A,BA,B and CC be subsets of UU such that U=110,A=44,B=27,C=47,ABC=90.\begin{aligned} & \lvert U \rvert =110, \lvert A \rvert =44, \lvert B \rvert =27, \\ & \lvert C \rvert =47, \lvert A \cup B \cup C \rvert=90. \end{aligned} If no element belongs to exactly two of the three subsets, what is the number of elements in the complement of ABC?A \cap B \cap C?

Consider a ground set UU and let X,YX,Y and ZZ be subsets of UU such that U=140,X=40,Y=35,Z=53,XY=7,YZ=10,ZX=15,XYZ=3.\begin{aligned} \lvert U \rvert & =140, \lvert X \rvert =40, \lvert Y \rvert =35, \lvert Z \rvert=53, \\ \lvert X \cap Y \rvert &=7, \lvert Y \cap Z \rvert=10, \lvert Z \cap X \rvert=15, \\ & \lvert X \cap Y \cap Z \rvert=3. \end{aligned} What is the number of elements in the complement of XYZ?X \cup Y \cup Z?

Given a universal set UU and subsets A,BA, B and CC of UU, which of the following is equivalent to the set {A(AcB)}{B(BC)}? \left\{ A\cap (A^{ c }\cup B) \right\} \cup \left\{ B\cap (B\cup C) \right\}?

100100 students took a quiz with the three problems Easy, Medium, and Challenge. 5252 solved Easy, 3535 students solved Medium, and 3232 students solved Challenge. Also, 3737 students solved exactly two out of the three problems and 1010 students solved all three problems. How many students solved none of the three problems?

Suppose AA, BB and CC are three sets such that AB=,A=9,B=9,A \cap B=\emptyset, \lvert A \rvert =9, \lvert B \rvert=9, C=6,AC=14,BC=10. \lvert C \rvert=6, \lvert A \cup C \rvert =14, \lvert B \cup C \rvert=10. What is the number of elements in the set ABC?A \cup B \cup C?

×

Problem Loading...

Note Loading...

Set Loading...