CBSE Class 11-science Answered

What it means by number of subset B of X & explain what is the logic behind taking step 2 in the image.

Asked by Vineeth K | 11 Apr, 2016, 05:18: PM

Expert Answer

straight X space equals space left curly bracket 1 comma 2 comma 3 comma.... comma 10 right curly bracket rightwards double arrow straight X space h a s space 10 space e l e m e n t s space s o space i t space h a s space 2 to the power of 10 space s u b s e t s. T h e space n u m b e r space o f space s u b s e t s space straight B space o f space straight X space s u c h space t h a t space straight A minus straight B space equals space left curly bracket 4 right curly bracket space m e a n s T h e space n u m b e r space o f space s u b s e t s left parenthesis straight B right parenthesis space o u t space o f space 2 to the power of 10 left parenthesis s u b s e t s space o f space straight X right parenthesis space w h i c h space s a t i s f i e s space t h e space c o n d i t i o n space space straight A minus straight B space equals space left curly bracket 4 right curly bracket. straight A minus straight B space equals space left curly bracket 4 right curly bracket rightwards double arrow space left curly bracket 4 right curly bracket element of straight A space b u t space left curly bracket 4 right curly bracket not an element of straight B F r o m space t h e space v e i n space d i a g r a m space w e space c a n space s e e space t h a t space t h e space e l e m t s space left curly bracket 1 comma 2 comma 3 comma 5 right curly bracket space o f space straight A space w i l l space a l w a y s space r e m a i n space i n space straight B. T h e space o t h e r space e l e m t s space o f space straight X space t h a t space c a n space b e space i n space straight B space c a n space b e space a n y space o f space t h e s e space left curly bracket 6 comma 7 comma 8 comma 9 comma 10 right curly bracket. I f space w e space t a k e space o t h e r space e l e m n t space o f space straight B space a s space 6 space w e space g e t space t w o space d i f f e r e n t space s e t s. space left curly bracket 1 comma 2 comma 3 comma 5 right curly bracket space a n d space space left curly bracket 1 comma 2 comma 3 comma 5 comma 6 right curly bracket space t h a t space m e a n s space 2 to the power of 1 space n u m b e r space o f space s u b s e t s. I f space w e space t a k e space o t h e r space e l e m n t space o f space straight B space a s space 6 space a n d space 7 space w e space g e t space f o u r space d i f f e r e n t space s e t s. space left curly bracket 1 comma 2 comma 3 comma 5 right curly bracket comma space left curly bracket 1 comma 2 comma 3 comma 5 comma 6 right curly bracket space comma space left curly bracket 1 comma 2 comma 3 comma 5 comma 7 right curly bracket space a n d space space left curly bracket 1 comma 2 comma 3 comma 5 comma 6 comma 7 right curly bracket space t h a t space m e a n s space 2 squared space n u m b e r space o f space s u b s e t s. S o space t h e r e space a r e space f i v e space e l e m t s space left curly bracket 6 comma 7 comma 8 comma 9 comma 10 right curly bracket space w h i c h space c a n space b e space i n space straight B space o f space straight X space s u c h space t a h t space straight A minus straight B space equals space left curly bracket 4 right curly bracket. H e n c e space t h e space n u m b e r space o f space s u b s e t s space a r e space space 2 to the power of 5.

Answered by Vijaykumar Wani | 12 Apr, 2016, 11:18: AM

CBSE Class 11-science Answered

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