Find Union and Intersection of Sets A, B, C and D
If \[ A=\{1,2,3,4,5\},\ B=\{4,5,6,7,8\}, \] \[ C=\{7,8,9,10,11\},\ D=\{10,11,12,13,14\} \] 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) \((A \cup D)\cap(B \cup C)\)
Solution
(i) \[ A \cup B=\{1,2,3,4,5,6,7,8\} \]
(ii) \[ A \cup C=\{1,2,3,4,5,7,8,9,10,11\} \]
(iii) \[ B \cup C=\{4,5,6,7,8,9,10,11\} \]
(iv) \[ B \cup D=\{4,5,6,7,8,10,11,12,13,14\} \]
(v) \[ A \cup B \cup C=\{1,2,3,4,5,6,7,8,9,10,11\} \]
(vi) \[ A \cup B \cup D=\{1,2,3,4,5,6,7,8,10,11,12,13,14\} \]
(vii) \[ B \cup C \cup D=\{4,5,6,7,8,9,10,11,12,13,14\} \]
(viii) \[ B \cup C=\{4,5,6,7,8,9,10,11\} \]
\[ A \cap (B \cup C)=\{4,5\} \]
(ix) \[ A \cap B=\{4,5\} \]
\[ B \cap C=\{7,8\} \]
\[ (A \cap B)\cap(B \cap C)=\Phi \]
(x) \[ A \cup D=\{1,2,3,4,5,10,11,12,13,14\} \]
\[ B \cup C=\{4,5,6,7,8,9,10,11\} \]
\[ (A \cup D)\cap(B \cup C)=\{4,5,10,11\} \]