Discrete Mathematics

Set Operations

Sets - Relative Complement

         

If AA and BB are subsets of the set U={0,3,5,10,12,16,18}U=\{0,3,5,10,12,16,18\} such that ABC={3,5},ACB={10,12},ACBC={16,18},A \cap B^{C}=\{3,5\}, A^{C} \cap B=\{10,12\}, A^{C} \cap B^{C}=\{16,18\}, then which of the following is equal to AB?A \cap B?

Details and assumptions

You may choose to read the summary page Set Notation.

Consider the ground set U={xx is a positive integer 17}.U=\{x \mid x \mbox{ is a positive integer } \leq 17\}. If A={1,2,,5}A=\{1,2,\ldots,5\} and BB is a subset of UU such that AB={4,5},(UA)(UB)={16,17},A \cap B=\{4, 5\}, (U \setminus A) \cap (U \setminus B)=\{16, 17\}, what is B?\lvert B \rvert?

Consider the ground set U={xx is a positive integer 35}U=\{x \mid x \mbox{ is a positive integer } \leq 35\} and let AA and BB be two subsets of UU such that A={1,2,3,,17},  A(AB)=A.A=\{1, 2, 3, \ldots, 17\}, \; A \setminus(A \setminus B)=A. What is (U\A)B?\lvert (U \backslash A) \cup B \rvert?

Details and assumptions

You may choose to read the summary page Set Notation.

Consider the sets A={x3x<50},B={xx0 or x>43}.A=\{x \mid 3 \leq x < 50\}, B=\{x \mid x \leq 0 \text{ or } x > 43\}. How many integers are there in the set AB?A \setminus B?

Details and assumptions

You may choose to read the summary page Set Notation.

Consider a ground set UU and let AA and BB be two subsets of U.U. If U=70,A=37,AB=13,AB=48, \lvert U \rvert=70, \lvert A \rvert=37, \lvert A \cap B \rvert=13, \lvert A \cup B \rvert=48, what is UBc? \lvert U \setminus B^c \rvert?

Details and assumptions

You may choose to read the summary page Set Notation.

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