Question

Choose the correct answer and give reason why its correct and please mention why other options are wrong​

Answer 1

Question:

The following sets  

A = {x : x is an integer, -1/2 < x < 9/2 } and

B = {x : x is a month of the year not having 31 days }

is equivalent to

(a) A = {0, 1, 2, 3} , B = {February, April, June, September, November}

(b) A = {0, 1, 2, 3, 4} , B = {February, April, June, September, November}

(c) A = {0, 3, 4} , B = {April, June, September, November}

(d) None of the above

Answer:

option (a) & option (b)

Step-by-step explanation:

Given :

• A = {x : x is an integer, -1/2 < x < 9/2 }

• B = {x : x is a month of the year not having 31 days }

To find :

the correct option among the given options

Solution :

➙ A = { x : x is an integer, -1/2 < x < 9/2 }

So, x is between -1/2 and 9/2

Let's convert the fraction into decimal form.

 -1/2 = -0.5

 9/2 = 4.5

Hence, -0.5 < x < 4.5

➙ B = { x : x is a month of the year not having 31 days }

There are 12 months in a year : January, February, March, April, May, June, July, August, September, October, November, December.

In these months,

• January, March, May, July, August, October, December are the months having 31 days.
• April, June, September, November are the months having 30 days.
• February is the month having 28 days (or) 29 days in a leap year.

The given set belongs to the months not having 31 days.

Hence B = {February, April, June, September, November}

Let's look at each option.

(a) A = {0, 1, 2, 3} , B = {February, April, June, September, November}

➙ A = {0, 1, 2, 3}

These integers are less than 4.5 and greater than -0.5

Hence, this is correct.

➙ B = {February, April, June, September, November}

These months are not having 31 days.

Hence, this is correct.

As both the sets are equivalent to the given option, This is the correct option.

(b) A = {0, 1, 2, 3, 4} , B = {February, April, June, September, November}

➙ A = {0, 1, 2, 3, 4}

These integers are less than 4.5 and greater than -0.5

Hence, this is correct.

➙ B = {February, April, June, September, November}

These months are not having 31 days.

Hence, this is correct.

As both the sets are equivalent to the given option, This is also the correct option.

(c) A = {0, 3, 4} , B = {April, June, September, November}

➙ A = {0, 3, 4}

These integers are less than 4.5 and greater than -0.5

Hence, this is correct.

➙ B = {April, June, September, November}

These months are not having 31 days. But February, a month which is also not having 31 days is not included in this set.

Hence, this is not correct.

As both the sets are not equivalent to the given option, This is not the correct option.