Provide a derivation for b A right arrow B C B A right arro

Provide a derivation for b) (A right arrow B) & C; (B A) right arrow D; (B right arrow A)/D

a) ~P->~Q is given

we will use the result that ~A->~B and B->A are equivalent

so, as ~P->~Q we can say that Q->P

using modus ponens, Q and Q->P we can say that P is true

as P is true PVR will definitely be true.

b) A->B &C is given

So, A->B is true (1)

C is true (2)

further, B->A is given (3)

from (1) and (3) we can say that A<->B (4) and also B<->A (5)

Given (B<->A) ->D (6)

from (5) and (6) using modus ponens rule we can conclude that D is true