Question

Which of the following sets are empty sets? Justify your answer.
The set of all triangles in a plane having the sum of their three angles less
T TRY THIS
1.
(i)
A = {x: = 4 and 3x = 9}.
than 180.​

Answer 1

Question no.1, Choice 1

$\sf{A=\{x|x^2=9\:and\:3x=9\}}$

It is a set having solutions as its element.

The common solution of two equations is $\sf{x=3}$.

An empty set has no elements. So, set A is not empty.

Question no.1, Choice 2

For choice 2, the elements are triangles on a plane. In a plane, all triangles have an angle sum of 180°.

The set has no elements. So, this is an empty set.

Question no.2

$\sf{B=\{x|x+5=5\}}$

It is a set having solutions as its element. There is one solution $\sf{x=0}$.

The set has one element, so it is not empty.

More information:

A set is a group of elements. If there are no elements in the set, it is called an empty set.

The notation of the number of elements in a set is $\sf{n(A)}$, when set A is given.

There are ways to show sets.

The set can be a list of elements. This is called Roster notation.

The set can be explained in mathematic phrases. This is called set-builder notation.

Answer 2

Question no.1, Choice 1

A =

$({x|x}^{2} = 9 \: and \: 3x = 9 )$

2

=9and3x=9}

It is a set having solutions as its element.

The common solution of two equations is \sf{x=3}x=3 .

An empty set has no elements. So, set A is not empty.

Question no.1, Choice 2

For choice 2, the elements are triangles on a plane. In a plane, all triangles have an angle sum of 180°.

The set has no elements. So, this is an empty set.

It is a set having solutions as its element. There is one solution \sf{x=0}x=0 .

The set has one element, so it is not empty.

More information:

A set is a group of elements. If there are no elements in the set, it is called an empty set.

The notation of the number of elements in a set is n(A) , when set A is given.

There are ways to show sets.

The set can be a list of elements. This is called Roster notation.

The set can be explained in mathematic phrases. This is called set-builder notation.