Question

Find S=set of all leap years. Between 1882 and 1906

Answer 1

Here, we first need to understand the exact definition of a Leap Year.In other words, we need to know what years are called Leap Years.


There are mainly two rules:

1) If the year is divisible by 4 and simulatneouslynot divisible by 100, then it is a leap year.

Eg. 2004, 2012, 1896, etc are Leap Years.


2) If the year is divisble by 100, (like 1800, 1900, 2000, etc) then it will be only considered a Leap Year if it is also divisible by 400.


Eg. 1600 is a Leap Year because it is divisible by 100 as well as 400.

But 1700, 1800, 1900 are NOT Leap Years, because they are divisible by 100 but not by 400.

Similarly, 2000 is a leap year. But 2100, 2200 and 2300 are Not Leap Years.




Thus, overall in a period of 400 years, we skip 3 Leap Years. This adjustment is what keeps our calendar and time clocks in sync with the actual Astronomical Motion.

[There is also a concept of Leap Second, where we add an extra second to keep us exactly in sync with Reality, but let's not go into it now]


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Let's come to your question. We have:

S = The set of all leap years between 1882 and 1906.


The leap years in that period are 1884, 1888, 1892, 1896, and 1904.

[Remember, 1900 is not a Leap Year, as it is divisble by 100 but not by 400]



So, we have:


S=\{1884 , \, 1888 , \,1892, \, 1896, \, 1904\}


There are five elements in Set S.

So, Cardinal Number of S is 5.