# Sample Solution_Set

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 .dot { height: 160px; width: 210px; border: 3px solid red; display: block; text-align:right; } .ven { margin-top:5px; margin-left:10px; float: left; width: 100px; height: 100px; border-radius: 50px; color: black; text-align: center; line-height: 10px; position: relative; } .one { background-color: rgba(0,0,255,0.4); line-height:100px; left:-65px;} .two::before{ content: 'x'; position: absolute; left:8px; line-height:100px } .two { background-color: rgba(255,0,0,0.4); margin-left: -100px; line-height:100px} U=119 A 69-x 39-x B 16 .dot { height: 160px; width: 210px; border: 3px solid red; display: block; text-align:right; } .ven { margin-top:5px; margin-left:10px; float: left; width: 100px; height: 100px; border-radius: 50px; color: black; text-align: center; line-height: 10px; position: relative; } .one { background-color: rgba(0,0,255,0.4); line-height:100px; left:-65px;} .two::before{ content: 'x'; position: absolute; left:8px; line-height:100px } .two { background-color: rgba(255,0,0,0.4); margin-left: -100px; line-height:100px} 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. .dot { height: 160px; width: 210px; border: 3px solid red; display: block; text-align:right; } .ven { margin-top:5px; margin-left:10px; float: left; width: 100px; height: 100px; border-radius: 50px; color: black; text-align: center; line-height: 10px; position: relative; } .one { background-color: rgba(0,0,255,0.4); line-height:100px; left:-65px;} .two::before{ content: '5'; position: absolute; left:8px; line-height:100px } .two { background-color: rgba(255,0,0,0.4); margin-left: -100px; line-height:100px} U=119 A 65 34 B 16 .dot { height: 160px; width: 210px; border: 3px solid red; display: block; text-align:right; } .ven { margin-top:5px; margin-left:10px; float: left; width: 100px; height: 100px; border-radius: 50px; color: black; text-align: center; line-height: 10px; position: relative; } .one { background-color: rgba(0,0,255,0.4); line-height:100px; left:-65px;} .two::before{ content: '5'; position: absolute; left:8px; line-height:100px } .two { background-color: rgba(255,0,0,0.4); margin-left: -100px; line-height:100px} U=119 A 65 34 B 16