I have to prove the following question,
Let A and B are subsets of a universal set U. Prove that A is a subset of B iff B' is a subset of A'
Now I don't understand how do I prove this using proof techniques. Please guide me.
We want to prove the following:
$$A\subseteq B\iff B^c\subseteq A^c$$
We need, therefore, to prove two implications.
Another approach is to use logical equivalence of $\alpha\rightarrow\beta\iff\lnot\beta\rightarrow\lnot\alpha$.
Since $A\subseteq B$ is $x\in A\rightarrow x\in B$, this as the above equivalence tells us, is the same as $x\notin B\rightarrow x\notin A$, which is precisely to say $B^c\subseteq A^c$.
See my formal proof at http://www.dcproof.com/MathSE-2011-09-30.htm
This proof was generated with the aid of my DC Proof software available at