3. (10 points) Consider the logical argument with premises: \"The sky is blue or birds can fly\", \"If birds can fly then so can bats\", \"If bats can fly or frogs can swim, then fish can ride bicycles\", \"Fish can't ride bicycles\" and conclusion: \"The sky is blue\"\nLet $p$ be the proposition \"The sky is blue\", $q$ be the proposition \"Birds can fly\", $r$ be the proposition \"Bats can fly\", $s$ be the proposition \"Frogs can swim\", and $t$ be the proposition \"Fish can ride bicycles\".
(a) Express the argument in propositional logic using the propositions defined above.
(b) Using the rules of inference and logical equivalences, prove the logical argument is valid.