Why phi is a subset of every set and what do you mean by proper subset?

Asked by himanshu sihag | 14th Jul, 2014, 06:09: AM

Expert Answer:

P h i space left parenthesis empty set right parenthesis space i s space a n space e m p t y space s e t space w h i c h space h a s space z e r o space e l e m e n t s. space A n y space s e t space w i l l space h a v e space s u b s e t s space w h i c h space h a v e space n u m b e r space o f space e l e m e n t s space r a n g i n g space f r o m space z e r o space t o space c o m p l e t e space s e t.  S o space a l l space s e t s space w i l l space h a v e space o n e space d e f i n i t e space s u b s e t space w i t h space z e r o space n u m b e r space o f space e l e m e n t s. space S o space p h i space i s space a space s u b s e t space o f space e v e r y space s e t. space  P r o p e r space S u b s e t : thin space A space p r o p e r space s u b s e t space i s space a space s u b s e t space o f space a space s e t space w h i c h space i s space n o t space e q u a l space t o space t h e space o r i g i n a l space s e t. space E x : space A equals left curly bracket 1 comma 2 comma 3 comma 4 comma 5 comma 6 right curly bracket comma space S u b s e t s space l i k e space left curly bracket 1 right curly bracket comma space left curly bracket 1 comma 2 right curly bracket comma... space e t c space a r e space p r o p e r space s u b s e t s space o f space A space e x c e p t space t h e space o r g i n a l space s e t. space A space i s space t h e space s u b s e t space o f space A space b u t space A space i s space n o t space p r o p e r space s u b s e t space o f space A. space space space

Answered by Dharma Teja | 14th Jul, 2014, 08:45: AM