SOLUTION: Prove πΆβˆ’π·=𝐢∩𝐷'. Just having a little bit of trouble with my wording of the proof. Thank you.

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Question 1206134: Prove πΆβˆ’π·=𝐢∩𝐷'. Just having a little bit of trouble with my wording of the proof. Thank you.
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be an element of the set  πΆβˆ’π·.

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  𝐢∩𝐷'.


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


In opposite, if x is an element of the set 𝐢∩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  𝐢∩𝐷'.


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


It implies that  C-D = 𝐢∩𝐷'.

At this point, the proof is complete.