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.  



 

RELATED QUESTIONS

1.  ~J v ~L
2.  ~(J * L) -> ~M
3.  ~E v (M v ~S)           /  ~(S * E)  (answered by jim_thompson5910)

1. ~ A v  ~ S					Basic Assumption		
2. ~ ~ S						Basic Assumption
3. (A => ~ O) & (~... (answered by mccravyedwin)

1. J v (K · L)
2. ~ K    //  J
 (answered by Edwin McCravy,math_tutor2020)

1. (E & I) v (M & U)			Basic Assumption
2. ~ E					Basic Assumption	/  ~ M => ~ U


 (answered by Solver92311)

Complete the truth table to show whether the following argument is valid or invalid. If... (answered by solver91311)

1. (I v K)>~L
2. (H v J) >I
3. ~K
4. H v K... (answered by jim_thompson5910)

1. (I v K) > ~L
2. (H v J) > I
3. ~K
4. H v K... (answered by jim_thompson5910)

Construct a proof for the following:

1. ~(J * L)

2. (J --> ~L) --> (~M * ~X)

3.... (answered by Edwin McCravy)

1. J>(G>L)
2.... (answered by solver91311)