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Complement of a Set

If A = 1, 2, ...

Question

If $A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} a n d D = {10, 11, 12, 13, 14} .$ Find:

(ix) $(A \cap B) \cap (B \cap C)$

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Solution

Given, $A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} a n d D = {10, 11, 12, 13, 14} .$
$(A \cap B) = {1, 2, 3, 4, 5} \cap {4, 5, 6, 7, 8}$

$(A \cap B) = {4, 5} . . . (1)$

Since $B = {4, 5, 6, 7, 8} a n d C = {7, 8, 9, 10, 11}$

Now, $(B \cap C) = {4, 5, 6, 7, 8} \cap {7, 8, 9, 10, 11}$

$(B \cap C) = {7, 8} . . . . (2)$

For $(A \cap B) \cap (B \cap C)$

From (1) & (2)

$(A \cap B) \cap (B \cap C) = {4, 5} \cap {7, 8}$

$(A \cap B) \cap (B \cap C) = ϕ$

Hence,

$(A \cap B) \cap (B \cap C) = ϕ$

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(i) If A = {1,2,3,4,5},

B= {4,5,6,7,8},

C= {7,8,9,10,11} and

D= {10,11,12,13,14}. Find :

(i) $A \cup B$ (ii) $A \cup C$

(iii) $B \cup C$ (iv) $B \cup D$

(v) $A \cup B \cup C$ (vi) $A \cup B \cup D$

(vii) $B \cup C \cup D$ (viii) $A \cap (B \cup C)$

(ix) $(A \cap B) \cap (B \cap C)$

(x) $(A \cup D) \cap (B \cup C)$

A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} a n d D = {10, 11, 12, 13, 14} .

(A \cup D) \cap (B \cup C)

A = {1, 2, 3, 4, 5}

B = {4, 5, 6, 7, 8}

C = {7, 8, 9, 10, 11}

D = {10, 11, 12, 13, 14}

A \cup B

A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} a n d D = {10, 11, 12, 13, 14} .

A \cup B \cup C

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