Answer
a.
~(p∧∼q)∨r
b.
~((p∧∼q)∧~r)
Work Step by Step
a.
p∧∼q→r
=~(p∧∼q)∨r Substitute using the equivalence p → q =∼p ∨ q, where p = (p∧∼q), and q = r
b.
Then using the new form: ~(p∧∼q)∨r
=~(~(~(p∧∼q)))∧~r) Substitute using the equivalence p ∨ q =∼(∼p∧ ∼q), where p = ~(p∧∼q) and q= r
=~((p∧∼q)∧~r) Simplify double inversions
