MHB Trouble determining truth value of logic statements

[chelseajjc95]

For the folowing two problems determine the truth value of each statement:
assume a and b are true and c and d are false.

not(a V b) -> s
not( T V T) -> s
F -> s
T

r -> [(d -> w) <-> (a ^ c )]
r -> [(F -> w) <-> ( T ^ F)]
r -> [T <-> F]
r -> F

I am fairly certain I did the first one correct but I would like some confirmation. The second one I am unsure how to evaluate
because the value of r is unknown and if r is t then the statement will be false but if r is false then the statement will be true.

 

[Evgeny.Makarov]

You are right: $r\to [(d\to w) \leftrightarrow (a\land c )]$ is equivalent to $\neg r$ under the assumptions about $a$, $b$, $c$ and $d$, so the original formula does not have a definite truth value.