Question

Write \[A = \left\{ {x|x} \right.\] is a month of the Gregorian year having more than 30 days\[\} \]in the roaster form:
A. \[A = \]{January, March, May, July, August, December}
B. \[A = \]{ January, March, May, June, August, October, December }
C. \[A = \]{ January, February, March, April, May, June, July, August, September, October, November, December }
D. None of these

Answer 1

Hint: We use the definition of Gregorian calendar and the information of the number of days in each month given in the Gregorian calendar. Find the months having number of days greater than 30 (not less or not equal to 30) and place them in a set form.

Complete step-by-step answer:
Since we know the Gregorian calendar is a calendar having 12 months: January, February, March, April,May, June, July, August, September, October, November and December.
We write number of days in each respective month in the Gregorian calendar
Number of days in January \[ = 31\]
Number of days in February\[ = 28\] or \[29\]
Number of days in March\[ = 31\]
Number of days in April \[ = 30\]
Number of days in May\[ = 31\]
Number of days in June \[ = 30\]
Number of days in July\[ = 31\]
Number of days in August\[ = 31\]
Number of days in September \[ = 30\]
Number of days in October\[ = 31\]
Number of days in November \[ = 30\]
Number of days in December\[ = 31\]
From the above mentioned list of number of days we can see the months having number of days greater than 30 are January, March, May, July, August, October and December
If we represent this data in roaster form we can write
\[A = \]{January, March, May, July, August, October, December} ……... (1)
Since, we don’t have any of the options from A., B. and C. matching the roaster form in equation (1).

\[\therefore \]Correct option is D.

Note: Gregorian calendar is a calendar having 12 months: January, February, March, April, May, June, July, August, September, October, November and December. It is a commonly used calendar around the world.
Roaster form of a set means writing the elements existing in the set separately in the set from.
Students might choose an incorrect option as many students learn that one month is of 30 days and next is of 31 days and then the sequence continues, but the consecutive months July and August both have 31 number of days so the calculation done by students on an earlier basis will be wrong.