CBSE Class 11-science Answered

Hello Sir, Please explain the below formulae with their venn diagrams. 1) A-B=A⇔A $intersection$ B=Ø 2) A $subset of or equal to$ B⇔B' $subset of or equal to$ A' 3) A $intersection$ (B $increment$ C)=(A $intersection$ B) $increment$ (A $intersection$ C)

Asked by seeni2005 | 19 Aug, 2020, 21:19: PM

Expert Answer

1) A-B=A⇔A

intersection

B=Ø

Suppose space straight A minus straight B equals straight A rightwards double arrow No space elements space from space straight A space has space been space removed space when space we space remove space the space elements space of space straight B space from space straight A This space means space that space there space is space no space element space in space straight B space which space is space common space to space straight A rightwards double arrow There space is space no space element space common space in space straight A space and space straight B rightwards double arrow straight A intersection straight B equals empty set Let apostrophe straight s space assume space straight A intersection straight B equals empty set rightwards double arrow space There space is space no space element space common space in space straight A space and space straight B comma space which space means space straight A space and space straight B space does space not space have space any space common space element So comma space if space we space take space straight A minus straight B comma space this space means space we space are space deleting space the space elements space of space straight A space which space are space in space straight B space also. But space as space there space is space no space element space of space straight A space which space is space in space straight B space rightwards double arrow space straight A minus straight B equals straight A space as space none space of space the space elements space of space straight A space has space been space deleted. Hence comma space straight A minus straight B equals straight A left right double arrow straight A intersection straight B equals empty set

2) A $subset of or equal to$ B⇔B' $subset of or equal to$ A'

$Suppose space straight A subset of or equal to straight B rightwards double arrow space Either space straight A equals straight B space or space straight A subset of straight B This space means comma space either space straight A space and space straight B space are space equal space or space straight B space contains space all space the space elements space of space straight A space and space straight A space does space not space have space all space the space elements space of space straight B rightwards double arrow Either space straight A equals straight B space or space straight B superset of straight A If space straight A equals straight B rightwards double arrow straight A apostrophe equals straight B apostrophe space... space left parenthesis straight i right parenthesis straight A apostrophe space will space have space elements space not space in space straight A space and space straight B apostrophe space will space have space elements space not space in space straight B As space straight A superset of straight B rightwards double arrow straight B apostrophe space will space have space elements space not space in space straight A space or space straight B As space straight A subset of straight B rightwards double arrow straight A apostrophe space will space have space elements space not space in space straight A space but space will space have space some space elements space of space straight B space which space are space not space in space straight A. rightwards double arrow straight A apostrophe superset of straight B apostrophe space... space left parenthesis ii right parenthesis So comma space from space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space have straight B apostrophe subset of or equal to straight A apostrophe$

3) A $intersection$ (B $increment$ C)=(A $intersection$ B) $increment$ (A $intersection$ C)

$straight B triangle straight C equals open parentheses straight B minus straight C close parentheses union open parentheses straight C minus straight B close parentheses straight A intersection open parentheses straight B triangle straight C close parentheses equals straight A intersection open square brackets open parentheses straight B minus straight C close parentheses union open parentheses straight C minus straight B close parentheses close square brackets equals open square brackets straight A intersection open parentheses straight B minus straight C close parentheses close square brackets union open square brackets straight A intersection open parentheses straight C minus straight B close parentheses close square brackets open parentheses straight A intersection straight B close parentheses triangle open parentheses straight A intersection straight C close parentheses equals open square brackets open parentheses straight A intersection straight B close parentheses minus open parentheses straight A intersection straight C close parentheses close square brackets union open square brackets open parentheses straight A intersection straight C close parentheses minus open parentheses straight A intersection straight B close parentheses close square brackets equals open square brackets straight A intersection open parentheses straight B minus straight C close parentheses close square brackets union open square brackets straight A intersection open parentheses straight C minus straight B close parentheses close square brackets Hence comma space straight A intersection open parentheses straight B triangle straight C close parentheses equals open parentheses straight A intersection straight B close parentheses triangle open parentheses straight A intersection straight C close parentheses$