Problem Solving Strategies (Two Sets)

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Below is a Venn diagram involving two sets A and B, in which the cardinalities are given as below
\(n_o(A)=p\)
\(n_o(B)=q\)
\(n(A \cap B)=r\)
\(n ( \overline{A \cup B})=s\)

1. कुनै पनि मन नपराउने संख्या : \(s\)
2. A र B दुबै मन पराउने संख्या: \(r\)
3. कुनै एउटा मात्र मन पराउने संख्या: \(p+q\)
4. A मात्र पराउने संख्या: \(p\)
5. B मात्र पराउने संख्या: \(q\)
6. A वा B मन पराउने संख्या: \(p+q+r\)
7. If cardinality of Set operations \(A,B,(A \cap B), (\overline{A \cup B})\) are given then use formula
   \(n(A \cup B)=n(A)+n(B)-n(A \cap B)\)
8. If cardinality of Set operations \(U, A,B,(A \cap B), (\overline{A \cup B})\) are given then use formula
   \(n(U)=n(A)+n(B)-n(A \cap B)+(\overline{A \cup B})\)
   Remember the concept:
   Total=\(A+B-(A∩B)+(\overline{A \cup B})\)
   
9. If cardinality of Set properties \(A_o,B_o,(A \cap B), (\overline{A \cup B})\) are given then use formula
   \(n(U)=n_o(A)+n_o(B)+n(A \cap B)+n(\overline{A \cup B})\)
   Remember the concept:
   Total=\(A_o+B_o+(A∩B)+(\overline{A \cup B})\)

Set Notation	Description	Figure	Formula
\(\phi\)	Empty Set		0
\(n(U)\)	Universal Set		p+q+r+s
\(n_o(A)\)	Only in A		p
\(n_o(B)\)	Only in B		r
\(n(\overline{A \cup B})\)	Nither in A nor in B		s
\(n(A \cap B)\)	Both in A and B		q
\(n(A)\)	Lies in A		p+q
\(n(B)\)	Lies in B		q+r
\(n(A \triangle B)\)	Lies only in A or only in B		p+r
\(n( \overline{A \triangle B})\)	Does not lie either only in A or only in B		q+s
\(n(\overline{A})\)	Does not lie on A		r+s
\(n(\overline{B})\)	Does not lie on B		p+s
\(n(A \cup B)\)	Lies in A or B		p+q+r
\(n (\overline{A})\)	Does not lie in only A		q+r+s
\(n (\overline{B})\)	Does not lie in only B		p+q+s
\(n(\overline{A \cap B})\)	Does not lie in both A and B		p+r+s