two sets having and n element respectively. the total no. of subsets of first set is 112 more than the total no. of subsets of second set. then the value of m+n-2 is???

Asked by Anu | 19th Jun, 2014, 12:48: PM

Expert Answer:

L e t space A space a n d space B space b e space t w o space s e t s space h a v i n g space m space a n d space n space e l e m e n t s space r e s p e c t i v e l y. space T h e r e f o r e comma space t h e space t o t a l space n o space o f space s u b s e t s space o f space A space a n d space B space a r e space 2 to the power of m space a n d space 2 to the power of n space r e s p e c t i v e l y. G i v e n space t h a t space t h e space t o t a l space n u m b e r space o f space s u b s e t s space o f space f i r s t space s e t space i s space 112 space m o r e space t h a n space t h e space t o t a l space n u m b e r space o f space s u b s e t s space o f space s e c o n d space s e t. rightwards double arrow 2 to the power of m equals 112 plus 2 to the power of n rightwards double arrow 2 to the power of m minus 2 to the power of n equals 112 rightwards double arrow 2 to the power of m minus 2 to the power of n equals 2 cross times 56 rightwards double arrow 2 to the power of m minus 1 end exponent minus 2 to the power of n minus 1 end exponent equals 8 cross times 7 rightwards double arrow 2 to the power of n minus 1 end exponent open parentheses 2 to the power of m minus 1 minus n plus 1 end exponent minus 1 close parentheses equals 2 cubed open parentheses 2 cubed minus 1 close parentheses rightwards double arrow 2 to the power of n minus 1 end exponent open parentheses 2 to the power of m minus n end exponent minus 1 close parentheses equals 2 cubed open parentheses 2 cubed minus 1 close parentheses rightwards double arrow n minus 1 equals 3 space a n d space m minus n equals 3 rightwards double arrow n equals 4 space a n d space m equals 7 rightwards double arrow m plus n minus 2 equals 7 plus 4 minus 2 equals 9

Answered by Vimala Ramamurthy | 19th Jun, 2014, 02:37: PM

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