Question

if A=(1, 2,3,4) and B=(3, 4,5,6) and C=(1, 2,4,6,7)
1.A-(BUC)
2.(A-B)U(B-C)​

Answer 1

Answer:

$A-(B \cup C) = \{\phi\}$

$(A-B) \cup(B - C) = \{1,2,3,5\}$

Given:

$A \: = \: \{1,2,3,4\}$

$B = \{3,4,5,6\}$

$C = \{1,2,4,6,7\}$

Explanation:

Part I

$A-(B \: \cup \: C)$

$B \: \cup \: C = \{1,2,3,4,5,6,7\}$

$A-(B \: \cup \: C) = \{1,2,3,4\} - \{1,2,3,4,5,6,7 \}$

$A-(B \: \cup \: C) = \{\phi\}$

Part II

$(A-B) \: \cup \: (B - C)$

$A-B = \{1,2\}$

$B - \: C = \{3,5\}$

$(A-B) \: \cup \: (B - C) = \{1,2,3,5\}$

Some Other Formulas:

$</u><u>1</u><u>)</u><u> </u><u>Power</u><u> \: set \: of \: a \: set = \: {2}^{n}$

$where \: n \: is \: the \: number \: of \:$

$elements \: in \: set$

$</u><u>2</u><u>)</u><u> </u><u>Subset</u><u> \: of \: a \: set = {2}^{n}$

$where \: n \: is \: the \: number \: of$

$elements \: in \: set$

$</u><u>3</u><u>)</u><u> </u><u>n</u><u>(A \: \cup \: B) = n(A) + n(B) - n(A \: \cap \: B)$

$</u><u>4</u><u>)</u><u> </u><u>n</u><u>(A-B) = n(A \: \cup \: B) - n(B) = n(A) - n(A \: \cap \: B)$

$</u><u>5</u><u>)</u><u> </u><u>n</u><u>(B-A) = n(A \: \cup \: B) - n(A) = n(B) - n(A \: \cap \: B)$

$</u><u>6</u><u>)</u><u> </u><u>n</u><u>(A \: \cup \: B) = n(A \: - \: B) - n(B - A) + n(A \: \cap \: B)$

$</u><u>7</u><u>)</u><u> </u><u>number</u><u> \: of \: elements \: which \: belong \: to \: exactly \: A \: or \: B = n(A-B) + n(B - A) = (n(A) - n(A \: \cap \: B)) + (n(B) - n(n(A \: \cap \: B))$

$\longrightarrow n(A) + n(B) - 2n(A \: \cap \: B)$

$</u><u>8</u><u>)</u><u> </u><u>n</u><u>(A') = n(\xi) - n(A)$