Solution to a. Let A and B be sets as follows, A= {1,2,3,5,7} and B = {1,5,6,8}. … - Sikademy
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a. Let A and B be sets as follows, A= {1,2,3,5,7} and B = {1,5,6,8}. Find: i. A∩B ii. | A∩B| iii. P(A∩B) iv. P(A) and P(B) v. | P(A) | and | P(B) | vi. The Cartesian product of A and B. vii. |A|, |B| and hence find |A x B|

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i.            A\cap B=\{1,5\}


ii.         A\cup B=\{1,2,3,5,6,7,8\}

|A\cup B=|=7


iii.       P(A\cap B)=P(\{1,5\})=\{\empty,\{1\}, \{5\},\{1,5\}\}  P(A∩B)


iv.        

P(A)=P(\{1,2,3,5, 7\})=\{\empty,\{1\}, \{2\},\{3\},\{5\},\{7\},\{1,2\},\{1,3\},\{1,5\},

\{1,7\},\{2,3\},\{2,5\},\{2,7\},\{3,5\},\{3,7\},\{5,7\},

\{1, 2,3\},\{1, 2,5\},\{1, 2,7\},\{1, 3,5\},\{1, 3,7\},

\{1, 5,7\},\{2, 3,5\},\{2, 3,7\},\{2, 5,7\},\{3, 5,7\},

\{1, 2,3,5\},\{1, 2,3,7\},\{1, 2,5,7\},\{1, 3,5, 7\},

\{2, 3,5,7\},\{1, 2,3,5,7\}\}

 

P(B)=P(\{1,5, 6,8\})=\{\empty,\{1\}, \{5\},\{6\},\{8\},\{1,5\},\{1,6\},\{1,8\},

\{5,6\},\{5,8\},\{6,8\},\{1,5, 6\},\{1,5, 8\},\{1,6,8\},

\{5, 6,8\},\{1, 5,6,8\}\}


v.    

|P(A)|=2^5=32

      

|P(B)|=2^4=16

vi.        

A\times B=\{(1,1), (1,5), (1,6), (1,8),(2,1), (2,5),(2,6), (2,8),(3,1), (3,5), (3,6), (3,8),

(5,1), (5,5), (5,6),(5,8),(7,1), (7,5), (7,6),(7,8)\}


vii.     

|A|=5, |B|=4

   


|A\times B|=5(4)=20


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Question ID: mtid-5-stid-8-sqid-3329-qpid-2028