## Comparative Analysis of Ethiopian and Gregorian Calendars' months

Comparative analysis of Ethiopian and Gregorian calendars’ months In mathematics, a set is a well-defined collection of things or objects. Let set A be the Ethiopian/ tropical calendar year that contains 12 months: 11 common months of 30 days and one special month of 35 and 36 days once in a leap year. Let another set B be the Julian /Gregorian/ temperate calendar year that contains 12 months: 7 months of 31 days (January, March, and May, July, August, October and December); 4 months of 30 days (April, June, September and November), and one special month of 28 or 29 days (February) once in a leap year.Therefore, Ethiopian/Tropical calendar and Julian /Gregorian/ temperate calendar years are equivalent. Each of them contains the same number of elements of months and days. But they are not equal sets because they have no the same elements or members. Therefore, the Ethiopian calendar months are not proper subset of the Gregorian or the Gregorian months are not the proper subset of the Ethiopian months. Moreover, suppose three categories of year are one, two and three shown in annexes 1, 2 and 3 are universal sets. In categories year one and two, subsets A and B separately contain 365 days, and in category year three each subset contains 366 days. The intersection of subsets A and B is the set of all members or elements of universal set which belong to both A and B.Thus the members of the intersection of A and B are 267,272, and 273 days in the first, second and third categories respectively [Please refer to diagrams 1, 2 and 3]. The union of two subsets is also an operation on sets. The union of set A and set B is the set of all elements of universal which belong to either to A or to B or to both. Thus the union of set A and set B in the first, second and third categories are 463,458 and 459 days respectively. In category year one, elements belong to either to set A or B is 98 days; and elements belong to both is 267. Therefore, the union of subsets A and B is 463 days (= 98+98+267). Similarly, the union of two sets in the second and forth categories year are 458 and 459 days (=93+93+272; =93+93+273) respectively. Finally, it is worthy to note that, the Period of Pagume has an intersection with September a period of five days (September 6-10) in the first and second categories of year, and six days (September 6-11) in the third category. Therefore, 5 or 6 days of Pagume cannot qualify to be the 13th month in the solar year system.

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