Question

A,B
and C are 3 sets such that AUB=
C and AnB=C & then

prove that A = C-B​

Answer 1

Step-by-step explanation:

If c denotes complement with respect to C , then A∩B=∅ can be rewritten as A⊆Bc .

On the other hand, A∪B=C implies Ac∩Bc=Cc=∅ (De Morgan), which is the same as Bc⊆A .

Hence A=Bc=C−B .

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