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.
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Proved, Proven

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

Quantity refers to the how much; number to the how many. "He purchased