Question 1033709
1. ~H & D  -------------hypothesis
2. ~H    -------------- simplification
3. H v (~T > R) --------hypothesis
4. ~T > R  --------------disjunctive syllogism on #2 and #3
5. H v (E > F) ----------hypothesis
6. E > F  ---------------disjunctive syllogism on #2 and #5
7. ~T v E ---------------hypothesis
8. T > E  ---------------material implication
9. T > F ----------------hypothetical syllogism on #8 and #6
10.  ~F > ~T ------------contrapositive of #9
11. ~F > R  -------------hypothetical syllogism on #10 and # 4
12. ~~F v R --------------material implication
13. F v R  ---------------double negation