if-x-A-100-and-x-B-75-x-AUB-50-then-find-x-A-B-and-x-B-A-

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))