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CBSE Class 11-science Answered

Prove that A intersection ( B - C ) = ( A intersection B ) - ( A intersection C )?
Asked by govtsecschoolnayaganv051 | 20 Jun, 2018, 06:41: PM
answered-by-expert Expert Answer
begin mathsize 16px style To space prove space that space colon space straight A space intersection space left parenthesis space straight B space minus space straight C space right parenthesis space equals space left parenthesis space straight A space intersection straight B space right parenthesis space minus space left parenthesis space straight A space intersection straight C space right parenthesis space Let space straight x space be space an space arbitrary space element space of space straight A space intersection space left parenthesis space straight B space minus space straight C space right parenthesis comma then space straight x space element of space straight A space and space straight x space element of space space left parenthesis space straight B space minus space straight C space right parenthesis rightwards double arrow straight x space element of space straight A space and space left parenthesis straight x space element of space straight B space and space straight x space not an element of space straight C right parenthesis rightwards double arrow left parenthesis straight x space element of space straight A space and space straight x space element of space straight B right parenthesis space and space left parenthesis space straight x space element of space straight A space and space straight x space not an element of space straight C right parenthesis rightwards double arrow straight x space element of space left parenthesis straight A space intersection straight B right parenthesis space and space straight x space not an element of space left parenthesis straight A space intersection space straight C right parenthesis rightwards double arrow straight x space element of left parenthesis straight A space intersection straight B right parenthesis space minus left parenthesis straight A space intersection space straight C right parenthesis Therefore comma space straight A space intersection space left parenthesis space straight B space minus space straight C space right parenthesis space subset of or equal to left parenthesis straight A space intersection straight B right parenthesis space minus left parenthesis straight A space intersection space straight C right parenthesis space... left parenthesis 1 right parenthesis Similarly space left parenthesis straight A space intersection straight B right parenthesis space minus left parenthesis straight A space intersection space straight C right parenthesis subset of or equal to straight A space intersection space left parenthesis space straight B space minus space straight C space...... left parenthesis 2 right parenthesis From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis comma space we space get straight A space intersection space left parenthesis space straight B space minus space straight C space right parenthesis space equals space left parenthesis space straight A space intersection straight B space right parenthesis space minus space left parenthesis space straight A space intersection straight C space right parenthesis space end style
Answered by Yasmeen Khan | 20 Jun, 2018, 07:13: PM

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