SOLUTION: Prove 𝐶−𝐷=𝐶∩𝐷'. Just having a little bit of trouble with my wording of the proof. Thank you.

Question 1206134: Prove 𝐶−𝐷=𝐶∩𝐷'. Just having a little bit of trouble with my wording of the proof. Thank you.
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
.


Let x be an element of the set  𝐶−𝐷.

It means that x does belong to C and does not belong to D.

In other words, x does belong to C and does belong to D'.

Hence, x belongs to the intersection  𝐶∩𝐷'.


   +----------------------------------------------+
   |           Thus we proved that                |
   |  the set C-D  is the subset of the set 𝐶∩𝐷'. |
   +--------------------------------------------- +


In opposite, if x is an element of the set 𝐶∩𝐷',
then x does belong to C and does belong to D'.

It means that x does belong to C and does not belong to D.

In other words, x does belong to the set C-D.

Hence, x belongs to  𝐶∩𝐷'.


   +-----------------------------------------------+
   |           Thus we proved that                 |
   |  the set 𝐶∩𝐷'  is the subset of the set C-D.  |
   +-----------------------------------------------+


It implies that  C-D = 𝐶∩𝐷'.

At this point, the proof is complete.

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