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 A∩BC={3,5},AC∩B={10,12},AC∩BC={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 A∩B?A \cap B?

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by Brilliant Staff

Consider the ground set U={x∣x 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 A∩B={4,5},(U∖A)∩(U∖B)={16,17},A \cap B=\{4, 5\}, (U \setminus A) \cap (U \setminus B)=\{16, 17\}, what is ∣B∣?\lvert B \rvert?

by Brilliant Staff

Consider the ground set U={x∣x 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∖(A∖B)=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.

by Brilliant Staff

Consider the sets A={x∣3≤x<50},B={x∣x≤0 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 A∖B?A \setminus B?

Details and assumptions

You may choose to read the summary page Set Notation.

by Brilliant Staff

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

Details and assumptions

You may choose to read the summary page Set Notation.

by Brilliant Staff
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