[noor123]

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Is CO2CH2CH3  an EWG or EDG?  That is when speaking about electrophilic aromatic substitution?
Also, what is the best way to know if a group is donating/withdrawing instead of  memorizing them all?

[kriggy]

its deactiwating group.
Usualy if it has free electron pair on atom bonded to benzene ring its activating group (alkyl group being one example I can think of which doesnt have free electron pair and is activating).
If it doesnt have electron pair or has positive charge its deactivating

[salteen]

The best way to tell if a group is donating or withdrawing is by drawing the possible resonance structures.  Try doing this for the compound you've proposed - what do you notice?

[noor123]

Yes, i have drawn the resonance structures, the electrons jumping down and the C=O being broken and added to the oxygen. Can you plz tell if my reasoning is correct,  So the Oxygen in C=O is more electronegative making the carbon partial positively charged, and same is the case with the other resonance structure that the carbon is still positive. Meaning that carbon is going to withdraw electrons from the ring. Am i correct?

[AromaticAcrobatic]

"So the Oxygen in C=O is more electronegative making the carbon partial positively charged"

^ Be careful there man, is more electronegative the right word?

Each carbon Oxygen bond has about 22 % ionic character making the carbonyl about 44% ionic. This  gives the carbonyl carbon more partial + character then in a single carbon oxygen bond. 
Oxygen is still withdrawing electrons with an electronegativity of 3.5 (Pauling scale). If Oxygen grabbed a proton then it would be more electronegative then usual.

[AromaticAcrobatic]

"Also, what is the best way to know if a group is donating/withdrawing instead of  memorizing them all?"

An easy way to think about this is, if there is an electrophile on the benzylic position it is ewd. Alkyl groups a weakly activatiing, if there is an atom that has lone pairs on the benzylic position but also particapates in resonace (not to the aromatic) is moderately activating and if there is an atom with lone pairs that is not participating in resonance (outside of the aromatic) then it is strongly activating.
Phenol is the strongest activator. If you an amide with a nitrogen substituent that is a phenyl then its moderately activating and like I said Alkyl groups are weakly donating. What you really need resonance structures for are the halogens. They are electron withdrawing but because they have more resonance structures for the ortho/para positions they are ortho/para directors. 
Oh yeah and if there is an atom with a full blown + charge then its strongly deactivating. 

You shouldn't just memorize things to memorize them, if you memorize something it should be because you looked at it that much and it just so happened to stick to your memory. Really, just understand how it works and you'll be fine.