SOLUTION: determine whether it is valid or invalid. If valid then give a proof. If invalid then give a counter example. A⊆B ⇒(B)^c⊆(A)^c. Where ()^c means complement.

Question 1074891: determine whether it is valid or invalid. If valid then give a proof. If invalid then give a counter example.
A⊆B ⇒(B)^c⊆(A)^c. Where ()^c means complement.
Answer by ikleyn(52874) (Show Source): You can put this solution on YOUR website!
.

Let U be a universal set which contains the sets (the subsets) A and B (and relative to which we consider complements).


Let x be the element of U which belongs to .

Then x does not belong to B, by the definition of a complement.

It implies that x does not belong to A (since A is a subset of B).

Hence, x belongs to , by the definition of a complement.


Thus we proved that EVERY element x which belongs to  belongs to  also.


It means that  is a subset of .


It is what has to be proved.


The proof is completed.

The problem is solved completely.

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SOLUTION: determine whether it is valid or invalid. If valid then give a proof. If invalid then give a counter example. A⊆B ⇒(B)^c⊆(A)^c. Where ()^c means complement.