#9 using discrete math and log equivalences

Show that (p AND q) rightarrow (p OR q) is a tautology using a series of logical equivalences. Show that (p OR q) AND (p OR r) rightarrow (q OR r) is a tautology using a series of logical equivalences. Show that p rightarrow (q rightarrow r) q rightarrow (p OR r) by showing (p rightarrow (q rightarrow r)) doubleheaded arrow (q rightarrow (p OR r)) is a tautology using a series of logical equivalences. Show that p doubleheaded arrow q p doubleheaded arrow q using a series of logical equivalences