What does this arrow symbol mean?

[roadrunner]

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 don't get those two columns because i don't 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!

 

[asd1249jf]

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.

 

[roadrunner]

ok i get that thanks
the other thing is tautology To
and contradiction's Fo

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

 

[roadrunner]

never miiind i drew tables and get them! :D

 

[roadrunner]

damn this crap is confusing!