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Consider the following sets: A = set ...

Consider the following sets:
A = set all rectangles in the same plane
B = set all squares in the same plane
C = set all parellegrams in the same plane
Find the following sets : `(i) A-B (ii) C-A (iii) A cap C (iv) B cap C (v) B cup C (Vi ) A cap B cup C `

Text Solution

Verified by Experts

We have
A = set all rectangles in the same plane
B = set all squares in the same plane
C = set all parellegrams in the same plane. Since all squares are rectangels `B sube A.`
Also all squares and rectagles are pareallelograms .
`So A, B sube C `
`therefore B sube A sube C`
(i) A - B= set of all rectangle which are not squares
(ii) C- A = set of all parallelograms which are not rectangles of squares
= set of all parallelograms which are not rectangles of squares
(iii) `A cap C`= set of all rectangles= A
(iv) `B cap C= `set of all squares = B
( v) `B cup C` = set of all parallelograms = C
(vi ) `A cap B cap `= set of all squares = B
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