   Question Answers

# Write $A = \{ x/x$ is a month of the Gregorian year having more than $30$days} in the roster form:A) ${\text{A = }}\left\{ {{\text{January, March, May, July, August, December}}} \right\}$B) ${\text{A = }}\left\{ {{\text{January, March, May, July, August, October, December}}} \right\}$C) ${\text{A = }}\left\{ {{\text{January,March, April, June, July, August, October,}}} \right\}$ D) None of these

Hint:At first, we will check the number of days of each month. From there we can identify the month which is having more than $30$ days.

It is given that; $A = \{ x/x$ is a month of the Gregorian year having more than $30$days}. We have to find it in roster form.
We know that:
Number of days in January is $31$ days.
Number of days in February is $28$ days (in leap year, it will be $29$ days).
Number of days in March is $31$ days.
Number of days in April is $30$ days.
Number of days in May is $31$ days.
Number of days in June is $30$ days.
Number of days in July is $31$ days.
Number of days in August is $31$ days.
Number of days in September is $30$ days.
Number of days in October is $31$ days.
Number of days in November is $30$ days.
Number of days in December is $31$ days.
So, we get the month which is having more than $30$ days: January, March, May, July, August, October, and December.
${\text{A = }}\left\{ {{\text{January, March, May, July, August, October, December}}} \right\}$

So, the correct answer is “Option B”.

Note:The Gregorian calendar is the calendar used in most of the world. It is named after Pope Gregory XIII, who introduced it in October $1582$.This calendar we use now.
In roster form, all the elements of a set are listed, the elements are being separated by commas and are enclosed within braces {}. It is also known as tabular form.