A quick way to answer this is to focus on the keyword pattern in the question rather than memorizing definitions from scratch. The phrase leaving double bonds or rings, or addition of groups to double bonds is a textbook signature for one enzyme class only.
Think of examples: pyruvate decarboxylase removes $CO_2$ from pyruvate without adding water, and a fumarase-type elimination step forms a double bond as part of the reaction. Reactions like these are catalyzed by lyases, not by hydrolases (which need water, like esterases or proteases), not by oxidoreductases (which need electron carriers such as $NAD^+/NADH$), and not by transferases (which shuttle a group like a phosphate or amino group between two substrates).
So working backward from the keywords, bond cleavage without water and without redox activity, generating a double bond or ring, is the lyase signature, and no other enzyme class fits that description.
\[\boxed{\text{Answer: (A) lyases}}\]