Discrete math. Show that (p→q)▼(q→r) and (p^q)→r are logically equivalent. My question is are they considered logically equivalent if the two propositional statements have the same truth tables?

Question

jim_thompson5910 · Answer

Yes, if two logical expressions have the same truth tables, then the logical expressions are equivalent (and vice versa). This is because the tables represent all of the possible combinations you can think of. 

It's like proving 2x = x+x to be true by writing out all of the numbers that satisfy that equation.

anonymous · Answer

Thanks Jim!

jim_thompson5910 · Answer

np

terenzreignz · Answer

But are they logically equivalent, though?

anonymous · Answer

The truth tables come out the same for the two statements. So they are right?

terenzreignz · Answer

Well, IF the truth tables are the same, then they must be equivalent.  Let me just double check...

terenzreignz · Answer

▼ is "or" right?

anonymous · Answer

upside down caret is or....how would I type it correctly?

terenzreignz · Answer

^ ?

terenzreignz · Answer

It's an 'and', then?

anonymous · Answer

^ is and, and upside ^ is or.

terenzreignz · Answer

Uhh..
$$\Large (p\rightarrow q) \lor(q\rightarrow r) \iff (p\land q) \rightarrow r$$
Is this it?

terenzreignz · Answer

a letter v would have sufficed haha

anonymous · Answer

Cool thanks. I got it solved.

terenzreignz · Answer

Equivalent?
Because if it's an 'or', they may not be...