Question

If p is true, q is false, and r is true, find the truth value of the statement.
r--------> (~p<---->~q)
The dotted lines are supposed to be solid.

Answer 1

fill in the blank: if p is true, then ~p is ________

Answer 2

false? I am not understanding how to do this at all.

Answer 3

good, if p is true, then ~p is false

~p (read as "not p") is the completely opposite of p

Answer 4

so if q is false, then ~q is true

Answer 5

true

Answer 6

~p<---->~q

turns into

false <--> true

and this entire thing is false because p <--> q is only true if both p and q are together true or false

Answer 7

so we go from this

r--------> (~p<---->~q)

to this

r --------> (false)

because r is true we can substitute that in to get

(true) ---> (false)

but this is false because p --> q is false when p = true, q = false

Answer 8

so the final answer is "false"

Answer 9

I am still not understanding how you got to your answer but I am going to apply what you have said and what the book says and see if i cant find a way to grasp it better. Thank you for your help.

Answer 10

just keep practicing and it will hopefully sink in a bit better