Provide a derivation for b P right arrow Q Q R Solutiona A

Provide a derivation for b) P right arrow Q; Q / R

a) A V C is true

hence, either A is true or C is true

Let A is true assume (1)

Then both AVC and AVB is true (2)

as AVB->D and AVC->~D . Since, (2) is true D is true as well as ~D is true. Hence we arrive at a contradiction.

so our assumtion (1) that A is true is false

we know AVC is true and A is false. Hence, C is true

b) P->Q and P is true

using modus ponens we can conclude that Q is true

given ~Q is true

so we again arrive at a contradiction as both Q and ~Q is true.

So we can conclude R.