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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Let A and B b...

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Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set X, show that A = B.

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A \cap X = B \cap X = ϕ

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A

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A \cap X = B \cap X = ϕ

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A = B

Let A and B be sets. If $A \cap X = B \cap X = Φ$ and $A \cup X = B \cup X$ for some set X. Show that $A = B .$

f

g

[0, a]

f (x) = f (a - x)

g (x) + g (a - x) = 4,

a \int 0 f (x) g (x) d x

Let A and B be sets. If A ∩ X = B ∩ X = Φ and A ∪ X = B ∪ X for some set X, show that A = B.

(Hints A = A ∩ (A ∪ X), B = B ∩ (B ∪ X) and use distributive law)

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