Capital Gains exemption on transfer of gifted property.

Can Capital Gains exemption be taken on transfer of a gifted property which was received as gift after the purchase of property which is to be claimed as exemption?

Mr. X received a property as gift from his parent in the current financial year (for e.g. 15th Oct 2020) Now Mr. X transfers this property resulting in Capital Gains.

Mr. X made payment for purchase of new property (assuming entire amount of capital gains invested) in the period of 1 year before the date of transfer (for e.g. on 1st Nov 2019). However purchase agreement for the same was made earlier than the 1 year before the date of transfer (for e.g 1st May 2019) Can Capital Gains exemption be taken in such case?

Further, Mr. X also owns another property. Will there be any implication in claiming Capital Gains exemption?