Given the expression:
(p $\implies$ q) $\wedge$ (q $\implies$ r)
I got rid of the implication to get:
(¬p $\vee$ q) $\wedge$ (¬q $\vee$ r)
I first drew 2 venn diagrams, the left hand side of the conjunction symbol then the right.
There are three sets, when I draw the 2 separately, do I draw just two circles, and then combine the two? Or do I start by drawing 3 circles, even though one set is not in the other?
If I draw the venn diagrams for both sides just using two circles, and then combine the two, I get a venn diagram with where everything outside the 3 sets are shaded. But if I started off with 3 circles, and then combine them due to the conjunction symbol, I get everything outside the 3 sets shaded and the part where all three sets share a common area.
Which one is correct?