Question

Do all 4 scenarios of the truth values have to be the same for something to be logically equivalent?

Answer 1

I have a truth table with two statements: ~p -> q and p v ~q
Putting them through the table of 4 truth value scenarios, I received the following:
~p -> q :
TT: T
TF: F
FT: T
FF: F

and
p v ~q
TT: T
TF: T
FT :F
FF: T

Answer 2

On your first table, if p is true ~p is false so ~p -> q is true if the left side is false
So your second entry there should be TF: T

Answer 3

Yes, all 4 scenarios have to be the same to be equivalent. And now they are.

Answer 4

I thought in conditional statements (p -> q) if the p = true, then the whole statement is true. So, if the first part is false, then the whole statement is false.

Answer 5

That thing is true in every case except one. You cannot have the left side true and the right side false.

Answer 6

This is from my text book: "Conditional If p, then q p → q True if the first part is true and the second part is true or if the first part is false.

Answer 7

Look at the table on this page.
http://www.regentsprep.org/Regents/math/geometry/GP1/ifthen.htm

Answer 8

So my table should look like:
1) ~p -> q :
TT: T
TF: F
FT: T
FF: T

and

2) p v ~q
TT: T
TF: T
FT :F
FF: T
But how can they be logically equivalent if table 1 goes TFTT and 2 goes TTFT