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Suppose Ai,Aii,Aiii......A30 are thirty sets each with five elements and Bi, Bii.......Bn  are n sets each with three elements.Let   U Ai=U Bj=S Please refer to rd sharma Pj 1.24 2016 edition
 
 
 
Assume that each element of S belongs to exactly 1o Ais and exactly 9 of Bjs.Find n
 
 
 
Please answer the question with explanation so that i could be able to understand
 
Please refer to Rd sharma for any mistake in the question after that let in the first line

Asked by Umang 20th May 2016, 10:49 PM
Answered by Expert
Answer:
H i comma
T h e r e space i s space n o space m i s t a k e space i n space t h e space q u e s t i o n.
S o l u t i o n colon
G i v e n space t h a t space t h e r e space a r e space 30 space s e t s space A subscript 1 comma space A subscript 2 comma space A subscript 3 comma... A subscript 30
E a c h space s e t space i s space h a v i n g space 5 space e l e m e n t s.
T h u s space t h e space t o t a l space n u m b e r space o f space e l e m e n t s space i n space a l l space t h e space s e t s comma space A subscript 1 comma space A subscript 2 comma space A subscript 3 comma... comma A subscript 30 space i s space 30 cross times 5 equals 150 space space space.... left parenthesis 1 right parenthesis
G i v e n space t h a t space S equals large union subscript i equals 1 end subscript superscript 30 A subscript i
T o t a l space n u m b e r space o f space e l e m e n t s space i n space S equals n left parenthesis S right parenthesis space space space space space... left parenthesis 2 right parenthesis
A l s o space g i v e n space t h a t space e a c h space e l e m e n t space o f space S space b e l o n g s space t o space e x a c t l y space 10 space A subscript i apostrophe s.
T h u s comma space w e space h a v e comma space n open parentheses S close parentheses cross times 10 equals 150
rightwards double arrow n open parentheses S close parentheses equals 150 over 10
rightwards double arrow n open parentheses S close parentheses equals 15 space space... left parenthesis 3 right parenthesis

A l s o space g i v e n space t h a t space S equals large union subscript j equals 1 end subscript superscript n B subscript j
E a c h space e l e m e n t space o f space S space b e l o n g s space t o space e x a c t l y space 9 space o f space B subscript j apostrophe s
T h e r e space a r e space 3 space e l e m e n t s space i n space e a c h space s e t space o f space B subscript j
T h u s comma space w e space h a v e comma space n open parentheses S close parentheses cross times 3 equals n
rightwards double arrow n equals 15 cross times 3 equals 45
Answered by Expert 23rd May 2016, 11:00 AM
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