Write down the power set of $C = \{1, \{2\}\}$.

  • A
    $\{\phi, \{1\}, \{\{2\}\}\}$
  • B
    $\{\phi, \{1\}, \{\{2\}\}, \{1, \{2\}\}\}$
  • C
    $\{\{1\}, \{\{2\}\}, \{1, \{2\}\}\}$
  • D
    None of these

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Out of $800$ boys in a school,$224$ played cricket,$240$ played hockey,and $336$ played basketball. Of the total,$64$ played both basketball and hockey,$80$ played cricket and basketball,and $40$ played cricket and hockey; $24$ played all three games. The number of boys who did not play any game is:

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If $U = \{2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$,$A = \{2, 4, 7\}$,$B = \{3, 5, 7, 9, 11\}$,and $C = \{7, 8, 9, 10, 11\}$,compute: $(A \cap U) \cap (B \cup C)$.

Which of the following statements is true?

If $A = \{a, b\}$,$B = \{c, d\}$,$C = \{d, e\}$,then the set $\{(a, c), (a, d), (a, e), (b, c), (b, d), (b, e)\}$ is equal to:

Consider the following relations:
$(1) \, A - B = A - (A \cap B)$
$(2) \, A = (A \cap B) \cup (A - B)$
$(3) \, A - (B \cup C) = (A - B) \cup (A - C)$
Which of these is/are correct?

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