Math  /  Discrete

QuestionGiven E={xIN/0x10}E=\{x \in I N / 0 \leq x \leq 10\} and the following subsets of E : A={1,2,4,8}B={0,1,2,3,5,8} and C={8,9,10}A=\{1,2,4,8\} \quad B=\{0,1,2,3,5,8\} \text { and } C=\{8,9,10\} a) Write EE in roster notation (in extension). b) Write A in builder notation (in comprehension). c) Write in extension: \begin{tabular}{|l|l|} \hlineABA \cap B & \\ \hlineABA \cup B & \\ \hline Aˉ\bar{A} & \\ \hline Bˉ\bar{B} & \\ \hlineAB\overline{A \cup B} & \\ \hlineAB\overline{A \cap B} & \\ \hline AˉBˉ\bar{A} \cap \bar{B} & \\ \hline AˉBˉ\bar{A} \cup \bar{B} & \\ \hlineA(BC)A \cup(B \cap C) & \\ \hline Note: & \\ \hline \end{tabular} d) Complete by: ϵ,,\epsilon, \notin, \subset and ⊄\not \subset. 1) {2}\{2\} \qquad ABA \cap B ii) 9. \qquad B iii) ACA \cup C \qquad B iv) ø \qquad A v) {1,3}\{1,3\} \qquad . BB
The symbol \in is a relation between element and set. The symbol \subset is a relation between 2 set. e) Draw Venn diagram that shows the elements of the given set. f) find: card (A): \qquad card (B): \qquad card (AC)(A \cup C) : \qquad card(AB)=\operatorname{card}(A \cap B)=

Studdy Solution
a) E={0,1,2,3,4,5,6,7,8,9,10}E = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} b) A={xNx=2n,n{0,1,2,3}}A = \{x \in \mathbb{N} \mid x = 2^n, n \in \{0, 1, 2, 3\}\} c) See 2.3. d) See 2.4. e) (Refer to a hand-drawn Venn diagram) f) card(A)=4\text{card}(A) = 4, card(B)=6\text{card}(B) = 6, card(AC)=6\text{card}(A \cup C) = 6, card(AB)=3\text{card}(A \cap B) = 3

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