Answer to Question #12797 in Discrete Mathematics for okunade ademola
Notice that A x B consists of all pairs (a,b), where a belongs to A,
and b belongs to B, while
B x A consists of all pairs (b,a), where a
belongs to A, and b belongs to B.
Let a belongs to A.
We should prove
that a belongs to B as well.
Take any b from B.
to A x B = B x A,
(a,b) = (b',a')
for some b' from B and a'
This means that
a=b' and b=a'.
Hence a belong to
This proves that A is contained in B.
By similar argument B is contained
in A, and so A=B.
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