If A - 1-2-3-4-5-B- 4-5-6-7-8 and C- 7-8-9-10-11 Find -i A- B ii A- Ciii B - C

(i) A = 1,2,3,4,5 B= 4,5,6,7,8 So, A ∪ B = x : x ϵ A or x ϵ B = 1,2,3,4,5,6,7,8 (ii) A ∪ C = x : x ϵ A or x ϵ C = 1,2,3,4,5,7,8,9,10,11 (iii) ...

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Standard VIII

Mathematics

Union of Sets

If A = 1,2,3,...

Question

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

B= {4,5,6,7,8} and C= {7,8,9,10,11}

Find :

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

(iii) $B \cup C$

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Solution

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

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

So, $A \cup B$ = { $x : x ϵ A o r x ϵ B$ }

= {1,2,3,4,5,6,7,8}

(ii) $A \cup C$ = { $x : x ϵ A o r x ϵ C$ }

= {1,2,3,4,5,7,8,9,10,11}

(iii) $B \cup C$ = { $x : x ϵ B o r x ϵ C$ }

= {4,5,6,7,8,9,10,11}

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Similar questions

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

Q. 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)

If A = {1, 2, 3}, B = {4} and C = {5}, then verify that :

(i) $A \times (B \cup C) = (A \times B) \cup (A \times C)$

(ii) $A \times (B \cap C) = (A \times B) \cap (A \times C)$

(iii) $A \times (B - C) = (A \times B) - (A \times C)$

If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find

(i) $A \times (B \cap C)$

(ii) $(A \times B) \cap (A \times C)$

(iii) $A \times (B \cup C)$

(iv) $(A \times B) \cup (A \times C)$

(a) If A = {1, 3, 4, 8, 9, 12}, B = {1, 4, 9} and C = {2, 4, 8, 10}

Find (i) A ∪ (B ∩ C) (ii) A ∩ (B ∪ C) (iii) (A ∪ B) ∩ (A ∪ C) (iv) (A ∩ B) ∪ (A ∩ C)

(b) If A = (2, 4, 6, 8, 10}, B = {1, 2, 3, 4, 5, 6} and C = (1, 3, 5, 7, 9, 11, 13}

Verify (i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

(iii) (A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C) (iv) (A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C)

Y = {x : x is an even number less than 12}

Z = {x : x is an odd number less than 12}

Show that (i) union of sets of distributive over intersection of sets.

(ii) intersection of sets is distributive over union of sets.

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If A = {1,2,3,4,5}, B= {4,5,6,7,8} and C= {7,8,9,10,11} Find : (i) A∪B (ii) A∪C (iii) B∪C

(i) A = {1,2,3,4,5} B= {4,5,6,7,8} So, A∪B = {x:x ϵ A or x ϵ B} = {1,2,3,4,5,6,7,8} (ii) A∪C = {x:x ϵ A or x ϵ C} = {1,2,3,4,5,7,8,9,10,11} (iii) B∪C = {x:x ϵ B or x ϵ C} = {4,5,6,7,8,9,10,11}

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

B= {4,5,6,7,8} and C= {7,8,9,10,11}

Find :

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

(iii) $B \cup C$

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

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

So, $A \cup B$ = { $x : x ϵ A o r x ϵ B$ }

= {1,2,3,4,5,6,7,8}

(ii) $A \cup C$ = { $x : x ϵ A o r x ϵ C$ }

= {1,2,3,4,5,7,8,9,10,11}

(iii) $B \cup C$ = { $x : x ϵ B o r x ϵ C$ }

= {4,5,6,7,8,9,10,11}