mathematical logic

Question

Which of the following are valid arguments?
A1:[P→(Q→R),Q]⟹(P→R)
A2:[(P→Q),(~Q→R),~R]⟹P

Comments

A1. is valid

A2 is contingency

Answer 1

A1:[P→(Q→R),Q]⟹(P→R)

=> [!P V !Q V R, Q]

=> !P V R

=> (P->R)

A2:[(P→Q),(~Q→R),~R]⟹P

By Modus Tollens, Q is conclusion. P can be 0/1 when Q is 1. So invalid.