Question

Write the following set using listing method and write whether it is finite or infinite. F={(a,b)|a,b€Q,a+b=11}

Answer 1

Step-by-step explanation:

Given:-

F={(a,b)|a,b€Q,a+b=11}

To find:-

Write the following set using listing method and write whether it is finite or infinite. F={(a,b)|a,b€Q,a+b=11}

Solution:-

Given set is F={(a,b)|a,b€Q,a+b=11}

From the given set a and b are rational numbers

and their sum is equal to 11

a+b = 11

11+0 = 11

0+11 = 11

10+1 = 11

1+10 = 11

9+2 = 11

2+9 = 11

3+8 = 11

8+3= 11

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.

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and 19/2+3/2=22/2 = 11

17/3+16/3 = 33/3=11

34/5+21/5=55/5=11

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If we can write this the list becomes an infinite

So the number of elements in the set F is infinite.

Answer:-

F={(a,b)|a,b€Q,a+b=11} is an infinite set.

Infinite set :-

A set having infinitely number of elements is called an infinite set.

Ex:-

Set of natural numbers

set of whole numbers

set of integers

....