What's symbolic logic got to do with it?

For (a => b) ^ (b => c) Where (=>) = "implies", (^) = Boolean AND (&)
For (+)=XOR, (v)=OR

Value,a,b,c,
True,T,T,T
True,T,T,F
True,T,F,T
True,T,F,F
True,F,T,T
True,F,T,F
True,F,F,T
True,F,F,F

What's the point? To analyze the "truth" value of statements in an argument, propositions and conclusions must agree. (Even the notation must agree consistently!)

"A tautology's truth is certain. A proposition's truth is possible. A contradiction's truth is impossible."
-Ludwig Wittgenstein, Tractatus Logico-Philosophicus, Vienna, 1918

More of the same shows how complex an analysis can become...

For (a=>b)^(b=>c)+(avb)=>c

Value,a,b,c,
True,T,T,T
False,T,T,F
True,T,F,T
False,T,F,F
True,F,T,T
False,F,T,F
True,F,F,T
False,F,F,F