119 जना विद्यार्थीहरुको सर्बेक्षणमा 16 जनाले पोखरा र लुम्बिनी दुबै मन पराउँदैनन्, 69 जनाले पोखरा र 39 जनाले लुम्बिनी मन पराउँछन (In a survey of 119 students, it was found that 16 like neither Pokhara nor Lumbini, 69 like Pokhara and 39 like Lumbini.
i. कति जनाले पोखरा मात्र मन पराउँछन् ? (How many students like Pokhara only?)
ii. कति जनाले लुम्बिनी मात्र मन पराउँछन् ? (How many students like Lumbini only?)
iii. माथिको तथ्याङ्कलाई भेनचित्रमा देखाउनुहोस् . (Show this above information in a Venn diagram.)
Solution
L=लुम्बिनि मन पराउने बिद्यार्थिको समुह | L=Set of students who like Lumbini | ||
अब, | Then | ||
n(U) = 119 | n(U) = 119 | ||
n (P∪L)' = 16 | n (P∪L)' = 16 | ||
n(P) = 69 | n(P) = 69 | ||
n(L) = 39 | n(L) = 39 | ||
मानौ, | n(P∩L) = x | Let, | n(P∩L) = x |
U=119 A
69-x
39-x
B
16
|
U=119 A
69-x
39-x
B
16
|
||
अब, | Venn-diagram को प्रयोग गर्दा | Then, | by using Venn-diagram, we can write |
69-x+x+39-x+16=119 | 69-x+x+39-x+16=119 | ||
or | x = 5 | or | x = 5 |
अब, | Now, | ||
पोखरा मात्र मन पराउने बिद्यार्थिको सँख्या= 69-x =64 | Students who like Pokhara only = 69-x =64 | ||
लुम्बिनि मात्र मन पराउने बिद्यार्थिको सँख्या = 39-x =34 | Students who like Lumbini only = 39-x =34 | ||
माथिको तथ्याङ्कलाई भेनचित्रमा तल देखाईएको छ। | The Venn-diagram for above information is given below. | ||
U=119 A
65
34
B
16
|
U=119 A
65
34
B
16
|
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