on solving we get given ER diagram
(EMP) _____ (manages) ___1___(DEPARTMENT)___1___(SPONSORED)______[PROJECT]
PROJECT has total participation but we don't know the mapping of it bw DEPARTMENT . So it can be either one to many or one to one
In case one to one , we required one table for (DEP)(SPONS)(PROJECT)
In case one to many , we required two table for (DEP)(SPONS)(PROJECT)
so we take worst case
EMP and DEP can have many one or one to one mapping. Instead of whatever the mapping , it can take two table
(EMP , MANAGES)
(DEP)
(PROJECT, SPONS)
TOTAL 3