Finding the Day of the Week

To find out the day of the week on 17th June 1998, we need to use the concept of the calendar. The calendar is a system that helps us keep track of days, weeks, months, and years. There are different types of calendars, but the most commonly used one is the Gregorian calendar.

The Gregorian calendar is a solar calendar that was introduced by Pope Gregory XIII in 1582. It is based on the Earth's orbit around the Sun and consists of 365 days in a year. However, every four years, an extra day is added to the calendar, known as a leap year, to account for the extra time it takes for the Earth to complete one orbit around the Sun.

Calculating the Day of the Week

To calculate the day of the week on 17th June 1998, we need to use a formula that involves the year, month, and day of the date in question. This formula is known as the Zeller's congruence formula.

Zeller's congruence formula is as follows:

h = (q + ((13(m+1))/5) + K + (K/4) + (J/4) - 2J) mod 7

Where
h = the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, and so on)
q = the day of the month (1 to 31)
m = the month (3 = March, 4 = April, 5 = May, and so on)
K = the year of the century (year mod 100)
J = the century (year/100)

Applying Zeller's Congruence Formula

Using Zeller's congruence formula, we can calculate the day of the week on 17th June 1998 as follows:

q = 17
m = 5 (June is the fifth month of the year)
K = 98 (1998 mod 100 = 98)
J = 19 (1998/100 = 19)

h = (17 + ((13(6+1))/5) + 98 + (98/4) + (19/4) - 2(19)) mod 7
h = (17 + 91/5 + 98 + 24.5 + 4.75 - 38) mod 7
h = (17 + 18.2 + 98 + 24.5 + 4.75 - 38) mod 7
h = 124.45 mod 7
h = 5.45

Since the value of h is not an integer, we need to round it up to the nearest whole number. Therefore, the day of the week on 17th June 1998 was Wednesday (option C).