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Statement 1: Joe tells you that he is an engineer and he studied in Mapua are logically equivalent to Statement 2: If Joe is lying, then Joe is not an engineer or he did not study in Mapua.
Because in the first case in statement 1 - " either I watched 'Crashlanding on You' or you watched 'Money Heist'" - it is condition "OR" but also "It is not true" - negation. In statement 2 "I did not watch 'Crashlanding on You' and you watched 'Money Heist'" equivalent to " either I watched 'Crashlanding on You' or you watched 'Money Heist'" but here it is not negation.