Q. 11 Let A and B be sets. If A X
B
X
and A
X
B
X for some set X, show that A
B.
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Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.
Given, A
X 
B 
X 
and A 
X 
B 
X
To prove: A = B
A = A
(A
X) (A 
X 
B 
X)
= A
(B
X)
= (A
B) 
(A
X)
= (A
B) 
(A 
X 
)
= (A
B)
B = B
(B
X) (A 
X 
B 
X)
= B
(A
X)
= (B
A) 
(B
X)
= (B
A) 
(B 
X 
)
= (B
A)
We know that (A
B) = (B
A) = A = B
Hence, A = B