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Hi Manasa:
Although Jim´s answer is of course correct, sometimes finding those cero thickness areas doesn`t resullt an easy task. When I've found myself in that situation, I've built a new part. A "kind of keel" which will intersect both halves allowing for the boolean union that is performed by the Symmetry(mirror) operator.
Click on the Troubleshooting Tips link in the second error message that you show. It will describe to you what zero thickness geometry is. You will have to examine your geometry and find where on the mirror plane the zero thickness condition exists and modify your original geometry so that condition does not exist when mirroring.
-Jim