To aggravate means to intensify, to make worse; to exasperate means to provoke, to irritate. “To aggravate the horrors of the scene.” “His remarks exasperated me.” “His conduct aggravates me” should be “His conduct annoys (or displeases, or irritates, or exasperates) me.”
Alleviate, Relieve
These words differ chiefly in degree. The latter is the stronger word.
Proposal, Proposition
A proposition implies consideration or discussion; a proposal contemplates acceptance or rejection. “Your proposition to build our new warehouse has received favorable consideration, and we are ready to receive your proposals.”
Providing, Provided
“You may go to skate, providing you first finish your task.” Incorrect. You should say provided.
Proven is sometimes incorrectly used for proved. “The evidence was complete and his guilt was fully proved.” Not proven is a legal term used in England to denote that the guilt of the accused is not made out, though not disproved.
Quantity, Number