if x(A)=100 and x(B)=75 x(AUB)=50 then find x(A−B) and x(B−A)


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Question Number 7324 by rohit meena last updated on 23/Aug/16

$i f x (A) = 100 a n d x (B) = 75$ $x (A U B) = 50$ $t h e n f i n d x (A - B) a n d x (B - A)$
Commented by Rasheed Soomro last updated on 23/Aug/16

$I m p o s s i b l e s i t u a t i o n$ $L e t x (A \cap B) = y$ $x (A - B) = 100 - y, x (B - A) = 75 - y$ $x (A - B) + x (A \cap B) + x (B - A) = x (A U B)$ $(100 - y) + y + (75 - y) = 50$ $175 - y = 50$ $y = 175 - 50 = 125$ $B u t y = x (A \cap B) ⩽ 75$ $H e n c e i m p o s s i b l e s i t u a t i o n .$
Commented by rohit meena last updated on 23/Aug/16

$k e s e$
Commented by Rasheed Soomro last updated on 24/Aug/16

$A \cup B c o n t a i n s a l l t h e m e m b e r s o f A$ $s o i t m u s t h a v e a t l e a s t 100 m e m b e r s (= x (A))$ $I t c a n n o t h a v e o n l y 50 m e m b e r s .$ $x (A \cup B) ⩾ m a x (x (A), x (B))$ $A l s o,$ $x (A \cap B) ⩽ m i n (x (A), x (B))$
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