Discrete mathematics: Please provide an explanation for your solution, as well.

1. All For 1 and One V (16 points) Let the domain of discourse contain only the two object a and b. For this problem only, you are allowed to use the following fake equivalence rules Ba P)P(a) V P(b) (a) [4 Points] Use a chain of equivalences to show that Q^ (3x P(z)) 3xQ^ P(z) (b) [6 Points] Likewise show that Q V (Bx P(x))3Q V P(x). (c) [2 Points] Are each of these equivalences also true assuming our fake equivalences? Yes or no. (d) 14 Points] Do the equivalences proven in (a)-(b) hold in every other domain of discourse? Briefly explain why or why not. 1. All For 1 and One V (16 points) Let the domain of discourse contain only the two object a and b. For this problem only, you are allowed to use the following fake equivalence rules Ba P)P(a) V P(b) (a) [4 Points] Use a chain of equivalences to show that Q^ (3x P(z)) 3xQ^ P(z) (b) [6 Points] Likewise show that Q V (Bx P(x))3Q V P(x). (c) [2 Points] Are each of these equivalences also true assuming our fake equivalences? Yes or no. (d) 14 Points] Do the equivalences proven in (a)-(b) hold in every other domain of discourse? Briefly explain why or why not