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Given a non-empty set X, consider the bi...

Given a non-empty set X, consider the binary operation `*: P(X)xx P(X) ->P(X)`given by `A * B = AnnB AAA , B in P(X)`is the power set of X. Show that X is the identity element for this operation and X is the only invertible element i

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Verified by Experts

Given defined :P(X)×P(X)→P(X)
and A∗B=A∩B,A,B∈P(X)
An element X is identify element for a binary operation
if
A∗X=A=X∗A
⟹A∩X=A=X∩A for A∈P(X)
Weknow that
A∗X=A=X∗A
...
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