Sets - Subsets

         

If S={2,6,8},S=\{2,6,8\}, which of the following is the power set of S?S?

A. {{2},{6},{8},{2,6},{2,8},{6,8},{2,6,8}} \{ \{2\}, \{6\}, \{8\}, \{2,6\}, \{2,8\},\{6,8\}, \{2,6,8\} \}

B. {,{2},{6},{8},{2,6},{2,8},{6,8},{2,6,8}} \{ \emptyset, \{2\}, \{6\}, \{8\}, \{2,6\}, \{2,8\},\{6,8\}, \{2,6,8\} \}

C. {,{2},{6},{8},{2,6},{2,8},{6,8}} \{ \emptyset, \{2\}, \{6\}, \{8\}, \{2,6\}, \{2,8\},\{6,8\} \}

D. {{2},{6},{8},{2,6},{2,8},{6,8}} \{ \{2\}, \{6\}, \{8\}, \{2,6\}, \{2,8\},\{6,8\} \}

Let X={6,α},Y={α2+5,α8,1}.X=\{6, -\alpha\}, Y=\{\alpha^2+5,\alpha-8,1\}. If XY,X \subseteq Y, what is the real number α?\alpha?

Given the set A={xx is a positive integer <13},A=\{x \mid x \text{ is a positive integer } < 13\}, how many subsets of AA have no even numbers?

Details and assumptions

The empty set \emptyset has no elements, and hence, has no even numbers.

If A={5,6,7}A=\{5, 6, 7\} and B={6,7,9,11,15},B=\{6, 7, 9, 11, 15\}, how many sets XX are there satisfying

(AB)X=X,(AB)X=X?(A-B) \cup X = X, (A \cup B) \cap X = X?

If AA is the set

A={5,7,11,14},A=\{5, 7, 11, 14\}, how many subsets of AA do not contain the element 7?7?

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