" डर सबैलाई लाग्छ तर सफल त्यहि व्यक्ति हुन्छ जाे डरकाे बावजुद अगाडि बढ्दछ ।", "A Teacher who is attempting to teach without inspiring the pupil with a desire to learn is hammering on cold iron". -Horace Mann

Class : 9 : Set

Set (समूह)


$\underline{\large \textbf{1. Important formulae:}}\\ 1. \normalsize \space n(A \cap B)=n(A)+n(B)-n(A \cup B)\\ 2. \normalsize \space n(U)=n(A)+n(B)-n(A \cap B)+ n \overline{(A \cup B)}\\ 3. \normalsize \space n_o(A)=n(A)-n(A \cap B)\\ 4. \normalsize \space n_o(B)=n(B)-n(A \cap B)\\ 5.\normalsize \space n(U)=n_o(A)+n_o(B)+n(A \cap B)+ n \overline{(A \cup B)}\\ 6. \normalsize \space n(A \cup B)=n_o(A)+n_o(B)+n(A \cap B)\\ 7. \normalsize \space n(\overline{A \cup B)}=n(U)-n(A \cup B)\\ $

Shaded the following parts of the sets by clicking the set notation.

Including three sets.
$ 8. \normalsize \space n(U)=n(A)+n(B)+n(C)-n(A \cap B)-n(B \cap C)-n(C \cap A) + n(A \cap B \cap C) + n \overline{(A \cup B \cup C)}\\ 9. \normalsize \space n(A \cup B \cup C)=n(A)+n(B)+n(C)-n(A \cap B)-n(B \cap C)-n(C \cap A) + n(A \cap B \cap C)\\ $ $\underline{\large \textbf{2. Illustrations:}}\\ $

1.

Here
मानाै, A र B ले क्रमशः स्वदेशी चिया र बिदेशी चिया मन पराउने मानिसहरुकाे समूहलाई जनाउँछ । U ले सर्वव्यापक समुह जनाउँछ भने

$n(U)=600\\ n(A)=300\\ n(B)=250\\ n(A \cap B)=150\\ \overline{n(A \cup B)}=?\\ \text{By the formula,}\\ \space n(U)=n(A)+n(B)-n(A \cap B) + \overline{n(A \cup B)}\\ \space or, 600=300+250-150+ \overline{n(A \cup B)}\\ \space or, 600=550-150 + \overline{n(A \cup B)}\\ \space or, 600=400 + \overline{n(A \cup B)}\\ \space or, \overline{n(A \cup B)}=600-400\\ \space \therefore \overline{n(A \cup B)}=200. ans.\\ $
माथिकाे तथ्याङ्कलाई भेन चित्रमा देखाउँदाः

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2.

Here
मानाै, A र B ले क्रमशः रेडियाे सुन्न र टेलिभिजन हेर्न मन पराउने मानिसहरुकाे समूहलाई जनाउँछ । U ले सर्वव्यापक समुह जनाउँछ भनेः
(Let A and B be the two non-empty sets who like to listen the radio and to watch the television respectively. If U Denotes universal set, then):

$n(U)=100 \% \\ n(A)=55 \% \\ n(B)=65 \% \\ n(A \cap B)=35 \% \\ \overline{n(A \cup B)}=?\\ $

(i) माथीकाे जानकारीलाई भेनचित्रमा देखाउँदा (Presenting in a Venn-Diagram):

(i) रेडियाे सुन्न र टेलिभिजन हेर्न मन नपराउने प्रतिशत (percentage of the people who do not like to listen the radio as well as to watch the television) $\overline{n(A \cup B)}$:

From the Venn-Diagram (भेन चित्रबाट):
$ \space \therefore \overline{n(A \cup B)}=15 \% $ ans.

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