Getting rid of plastic bags

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There are movements being organized each day in several major cities worldwide to get rid of plastic bags. These movements are quick to point out that the plastic bags from the grocery store that we throw away are polluting our oceans and our soil because it takes years for them to decompose, therefore we must get rid of them by replacing them with paper bags which can decompose easily. But using paper bags means we have to cut down more trees because trees are the main source of material to produce paper. So, should we stop using plastics bags? Or do we just have to learn to manage their proper disposal?