If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8} and C = {10, 11, 12, 13, 14}, find:

Question:

If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8} and C = {10, 11, 12, 13, 14}, find

(i) $A \cup B$

(ii) $\mathrm{B} \cup \mathrm{C}$

(iii) $\mathrm{A} \cup \mathrm{C}$

(iv) $B \cup D$

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

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

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

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

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

Solution:

Given; A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8} and C = {10, 11, 12, 13, 14}

(i) A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8}

(ii) $B \cup C=\{4,5,6,7,8,10,11,12,13,14\}$

(iii) $\mathrm{A} \cup \mathrm{C}=\{1,2,3,4,5,10,11,12,13,14\}$

(iv) $B \cup D$

(v) $(\mathrm{A} \cup \mathrm{B}) \cup \mathrm{C}=\{1,2,3,4,5,6,7,8,10,11,12,13,14\}$

(vi) $(A \cup B) \cap C=\Phi$ or \{\}

(vii) $(A \cap B) \cup D=$

(viii) $(A \cap B) \cup(B \cap C)=\Phi$ or \{\}

(ix) $(A \cap C) \cap(C \cup D=$

 

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