- #1

mathmari

Gold Member

MHB

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I have proven the following properties:

(i) $(a\Rightarrow b)\iff (\neg b\Rightarrow \neg a)$

(ii) $[(a\Rightarrow b)\land (b\Rightarrow c)]\Rightarrow (a\Rightarrow c)$

(iii) $[a\land (a\Rightarrow b)]\Rightarrow b$

At the second part of the exercise we have to show the de Morgan rules:

- $C_X(A\cup B)=(C_XA)\cap (C_XB)$

- $C_X(A\cap B)=(C_XA)\cup (C_XB)$

where $A,B$ are subsets of $X$ and $C_X$ is the complement in $X$. Is the first part relevant, i.e. do we have to use the first part to show these rules? Or is this not possible and we have to show that as usual taking an element of the lft set and showing that it is in the right set and also other way around?