Is This Propositional Logic Formulation Correct for Validating the Argument?

[Rytif]

1. Problem
Directions: Using propositional logic, prove that each argument is valid. Use the statement letters shown.

If the birds are flying south and the leaves are turning, then it must be fall. Fall brings cold weather. The leaves are turning but the weather is not cold. Therefore the birds are not flying south. B, L, F, C2. The attempt at a solution

B = birds flying south.
L = leaves are turning.
F = is fall.
C = it is cold.

[(B & L)->F] & (F->C) & (L & C')->(B')

(I'm just wondering if I have the correct logic without proving it yet)I appreciate it, thanks.

 

[Office_Shredder]

It doesn't seem to me like you want a single statement. Moreso something like assume all of these are true:

(B & L)->F
F->C
L & C'

as three separate statements, and your objective is to prove that B' is true