Which sentence is correct:
Why don't you try to give up candy if you want to lose some weight?
Why don't you try giving up candy if you want to lose some weight?
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Both sentences are correct. They have a different meaning.
“Try to” implies that the action that is attempted may or may not succeed. Try to give up candy; maybe you will succeed in refraining from eating candy, or maybe you will succumb to the temptation and eat candy anyway.
“Try + -ing” indicates that the action may or may not have the desired result. Try giving up candy; if you do give up candy, maybe you will lose weight, or maybe you will not.