SOLUTION: determine whether it is valid or invalid. If valid then give a proof. If invalid then give a counter example. A&#8838;B &#8658;(B)^c&#8838;(A)^c. Where ()^c means complement.

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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(52873) (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.

SOLUTION: determine whether it is valid or invalid. If valid then give a proof. If invalid then give a counter example. A&#8838;B &#8658;(B)^c&#8838;(A)^c. Where ()^c means complement.

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.