If $A = \{ x : x \text{ is an integer and } x^2 - 9 = 0 \}$,$B = \{ x : x \text{ is a natural number and } 2 \leq x < 5 \}$,and $C = \{ x : x \text{ is a prime number } \leq 4 \}$,then $(B - C) \cup A$ is:

  • A
    $\{ -3, 3, 4 \}$
  • B
    $\{ 2, 3, 4 \}$
  • C
    $\{ 3, 4, 5 \}$
  • D
    $\{ 2, 3, 5 \}$

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

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If $A = \{2, 3, 4, 8, 10\}, B = \{3, 4, 5, 10, 12\}, C = \{4, 5, 6, 12, 14\}$,then $(A \cup B) \cap (A \cup C)$ is equal to:

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