A "Child's Annuity" shall be payable monthly after the death of an employee parent to the unmarried child until the child's attainment of age 18, under the following conditions, if the child was born before the employee attained age 65, and before he withdrew from service:
(a) Upon death resulting from injury incurred in the performance of an act of duty;(b) Upon death in service from any cause other than injury incurred in the performance of an act of duty, if the employee has at least 4 years of service after the date of his original entry into service, and at least 2 years after the date of his latest re-entry;(c) Upon death of an employee who withdraws from service after age 50 (age 55 if withdrawal was before January 1, 1988), and who has entered upon or is eligible for annuity. The first payment shall become due and payable one month after the date of death.