Question 1029119
1. T ∨ (P ∨ S)-----------------Hypothesis
2. ~T        ------------------Hypothesis
3.  P ∨ S    ------------------Disjunctive syllogism on #1 and #2
4. ~T ⊃ (S ⊃ L) ---------------Hypothesis
5. S ⊃ L       ---------------modus ponens on #2 and #4
6.  ~~P∨S --------------double negation on #3
7.  ~P⊃S ---------------material implication on #6
8.  ~P⊃L-------------- hypothetical syllogism on #5 and #7
9.  ~L⊃P --------------contrapositive of #8
10.  P⊃Q --------------Hypothesis
11.  ~L⊃Q  -------------hypothetical syllogism on #9 and #10
12.  ~~L∨Q -------------material implication on #11
13.  L∨Q  -------------double negation 
14.  Q∨L  --------------commutativity