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(aub)-c=(a-c)u(b-c).prove it?

Asked by Biffi 24th September 2016, 7:43 PM
Answered by Expert
Answer:
begin mathsize 16px style Now comma space left parenthesis straight B minus straight C right parenthesis space equals space left curly bracket any space element space straight x space in space straight B space and space straight x space not space in space straight C right curly bracket space space
left parenthesis straight A minus straight C right parenthesis space union space left parenthesis straight B minus straight C right parenthesis space equals space left curly bracket straight x space in space straight A space and space straight x space not space in space straight C right curly bracket space or space left curly bracket straight x space in space straight B space and space straight x space not space in space straight C right curly bracket space space
Both space those space sets space include space straight x space not space in space straight C comma space so space we space can space " factor " space that space out colon space space space
left parenthesis straight A minus straight C right parenthesis space union space left parenthesis straight B minus straight C right parenthesis space equals space left curly bracket straight x space not space in space straight C right curly bracket space and space left parenthesis left curly bracket straight x space in space straight A right curly bracket space or space left curly bracket straight x space in space straight B right curly bracket right parenthesis space space space
Now space the space RHS space is space just space union space of space straight A space and space straight B comma space so space we space have colon space space space
LHS space equals space left parenthesis straight A minus straight C right parenthesis space union space left parenthesis straight B minus straight C right parenthesis
space space space space space space space space space equals space left curly bracket straight x space not space in space straight C right curly bracket space and space left parenthesis straight x space in space straight A union straight B right parenthesis
space space space space space space space space space equals space left parenthesis straight A union straight B right parenthesis space minus space straight C space space space space space space space which space is space obtained space by space interchanging space the space terms
space space space space space space space space space equals space RHS space
Hence space proved. end style
Answered by Expert 25th September 2016, 9:59 AM
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