What does this symbol mean?

1. Oct 4, 2007

i am doing truth tables in a comp sci course and unsure as to what <--> and --> mean
for example

p-->q boook says p implies q
p<-->q boook says biconditional of two statements

truth table sshown is as folllowes

p w p-->q p<-->q
0 0 1 1
0 1 1 0
1 0 0 0
1 1 1 1

i dont get those two columns because i dont understand what the "-->" and "<-->" notations mean
i think the last one just means that p/q either both have to be truw or both half to be false?

thanks!

2. Oct 4, 2007

l46kok

For the implification statement, -->, this is the semantic of it:

If P is true, then the proposition is whatever Q is. Else, the proposition is true.

Here is an example : Suppose P is false, then p-->q turns out to be true regardless of what q is.

Suppose P is true and Q is true then p-->q turns out to be true.

Suppose P is true and Q is false then p--q turns out to be false.

And as for p<-->q, yes you are right. Other way of reading that as if you have an odd number of true in your truth table, then the logic is false and if you have even number of true, then logic is true.

3. Oct 4, 2007

ok i get that thanks
the other thing is tautology To

how do these make sense

p \/ Fo <==>P
p /\ To <==>P

p\/(not)p<==>To
p/\(not)p<==>Fo

p\/(p/\q)<==>p
p/\(p\/q)<==>p

make sense

Last edited: Oct 4, 2007
4. Oct 4, 2007