Answer
a.
~(p∨~q)∨(r∨q)
b.
~(~(~p∧q)∧(~r∧~q))
Work Step by Step
A.
p∨~q → r∨q = ~(p∨~q)∨(r∨q) substitute using the equivalence p → q =∼p ∨ q with (p∨~q) = p and (r∨q) = p
B.
Using the form from part a
~(p∨~q)∨(r∨q) = ~(~(~p∧~(~q)))∨(r∨q) substitute using the equivalence p∨q=∼(∼p∧∼q) , with p = p and q = ~q
=(~p∧q)∨(r∨q) Simplify double inversions
=(~p∧q)∨~(~r∧~q) substitute using the equivalence p∨q=∼(∼p∧∼q) , with r = p and ~q = q
=~(~(~p∧q)∧~(~(~r∧~q))) substitute using the equivalence p∨q=∼(∼p∧∼q) , with (~p∧q) = p and ~(~r∧~q) = q
=~(~(~p∧q)∧(~r∧~q)) Simplifying double inversions
