I have a math question that is just driving me nuts.
If it is true that if price goes up then usually all wages go up, then if the price of steel goes up then labor wage goes up. If the price of steel goes up, then the sales of cars goes down. If labor wage doesn't go up then the sales of household goods goes down, which means we are in a recession. Therefore, the price of steel goes up and we are in a recession.
Here's what I did so far:
P: price goes up
Q: all wages go up
R: the price of steel goes up
S: labor wage goes up
T: the sales of cars goes down
U: the sales of household goods goes down
V: we are in a recession
(P => Q) => (R => S)
R => T
( ~S => ( U and T) ) => V
_______________________________
R and V
Is my notation correct? I want to prove if the conclusion is correct (tautology). I can just use the truth table ( using wolframalpha is the easist way to go about it). But how to solve it using rule of inference?