SOLUTION: 1. J => (L v T) Basic Assumption 2. ~ (L v ~ J) Basic Assumption / ~ L => T

1. J ==> (L v T)      Premise

2.  ~(L v ~J)         Premise

// Prove: ~L ==> T



3. ~L & J             2, DeMorgan's (DeM)

4. J                  3, Simplification (SIMP)

5. L v T              4,1, Modus Ponens (MP) 

6. ~L ==> T           5, Material Implication (MI)



---------- DONE ----------



In words:

3.  "Not (L or (not J))" true means we can say equivalently "(not L) AND (J)" is true.  Draw a truth table if not convinced.

4.  Since "(not L) and J" is true, we can say "J is true" (we can also say "not L" is true but we don't need that in this proof).

5.  Given J is true, it follows "L or T" is true, by premise #1.

6.  "L or T" true is the same as  "if (not L) then T".   Draw a truth table if not convinced.