If A - 5- 6- 7- 8- 9 - B - x-3-x-8-and-x-W and C- x-x-5-and-x-N - Find- iA - B-and-A - B-C ii B - C-and-A - B - C iii A - B-and-A - B- C iv B - C-and-A - B - C Is A - B- C - A - B - C - Is A - B- C - A - B - C -

A = (5, 6, 7, 8, 9) B = (4, 5, 6, 7) C = (1, 2, 3, 4, 5) (i) A ∪ B= (4, 5, 6, 7, 8, 9) A ∪ B and (A ∪ B) ∪ C=(1, 2, 3, 4, 5, 6, 7, 8, 9) (ii) B ∪ C = (1, 2 ...

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Byju's Answer

Standard VIII

Mathematics

Intersection of Sets

If A = 5, 6, ...

Question

If A = ${5, 6, 7, 8, 9}$ , B = ${x : 3 < x < 8 a n d x \in W}$ and C= ${x : x \leq 5 a n d x \in N}$ . Find:

(i) $A \cup B a n d (A \cup B) \cup C$

(ii) $B \cup C a n d A \cup (B \cup C)$

(iii) $A \cap B a n d (A \cup B) \cap C$

(iv) $B \cap C a n d A \cap (B \cap C)$

Is $(A \cup B) \cup$ C = A $\cup (B \cup C)$ ?

Is $(A \cap B) \cap C$ = A $\cap (B \cap C)$ ?

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Solution

A = (5, 6, 7, 8, 9) B = (4, 5, 6, 7) C = (1, 2, 3, 4, 5) (i) $A \cup B$ = (4, 5, 6, 7, 8, 9)

$A \cup B a n d (A \cup B) \cup$ ~C=(1, 2, 3, 4, 5, 6, 7, 8, 9)

(ii) $B \cup C$ = (1, 2, 3, 4, 5, 6, 7)

$A \cup (B \cup C)$ = (1, 2, 3, 4, 5, 6, 7, 8, 9)

(iii) $A \cap B = (5, 6, 7) (A \cap B) \cap C = (5)$

(iv) $B \cap C = (4, 5) A \cap (B \cap C) = (5)$

(v) $(A \cup B) \cup C = (1, 2, 3, 4, 5, 6, 7, 8, 9)$

$A \cup (B \cup C) = (1, 2, 3, 4, 5, 6, 7, 8, 9)$

Yes, these are equal.

(vi) $(A \cap B) \cap C = A \cap (B \cap C)$

${5} = {5}$

Yes, these are equal

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If A = {5,6,7,8,9}, B = {x:3 < x < 8 and x ∈ W} and C= {x:x ≤ 5 and x ∈ N}. Find: (i)A∪B and (A∪B) ∪ C (ii) B∪C and A∪(B∪C) (iii) A∩B and (A∪B)∩C (iv) B∩C and A∩(B∩C) Is (A∪B)∪ C = A ∪(B∪C) ? Is (A∩B)∩C = A ∩(B∩C) ?