7. Use previously proven logical equivalencies to prove each of the following logical equivalencies about conditionals with conjunctions: (b) [P- → (Q ^ R)] = (P → Q) ^ (P → R)

Conditional Statement p --> q      (If p, then q) Converse                   q --> p      (If q, then p) Inverse                    ~p --> ~q    (If not p, then not q) Contrapositive          ~q --> ~p    (If not q, then not p) Select a problem/statement from the ones listed below that hasn't been discussed and answer the following questions: 1. Write the problem as conditional statement (if is not under this form) 2. Write the converse 3. Write the inverse 4. Write the contrapositive statement The statements are: 1. If beauty were a minute, then you would be an hour. 2. If you lead, then I will follow. 3. If it ain't broke, don't fix it. 4. If I had a nickel for each time that happened, I will be rich. 5. if you build it, he will come 6. Where is smoke, there is fire 7. If eagles can fly, then eagles are fish 8. If Honk Kong is in China, then Tokyo is in Japan 9. If 7+5=12, then America has a queen 10. When I am hungry, I eat.

Match each of the following compound propositions with the logically equivalent one. (pV¬q) P→→q (p → a) (p^(-(p^ q))) 1. ¬p/q 2. p V q 3. pVq 4. p -q