Question

A={1,2,3,4,5,6}
{1,2,3}£A
£ means a belongs to the set X
Please tell true at false
If false then explain​

Answer 1

Step-by-step explanation:

Given:-

A={1,2,3,4,5,6} {1,2,3}€A

€ - belongs to

To find:-

Is {1,2,3}€A true or false

Solution:-

Given set = {1,2,3,4,5,6}

and {1,2,3} € A

It is false .

The elements of the set {1,2,3} are in the set A

{1,2,3} is the one of the subsets of the set .

If an element is in the given set then the element belongs to the given set.

Given set contains 6 elements

n(A)=6

Total possible subsets to the set A = 2^6 = 32

{1,2,3} is the subset of the set A .

So it does not belongs to the given set A

It is true when A is given in the form of Power set.

The only relation between the given sets is

{1,2,3} is sub set of {1,2,3,4,5,6}

Answer:-

It is false

Used formulae:-

• If an element in the given set then the element belongs to the given set.
• If all elements in A are in B then A is said to be a subset of the set B .
• The total number of subsets in the set A of 'n' elements is 2^n.

Answer 2

$\large\underline{\bold{Given \:Question - }}$

A={1,2,3,4,5,6} and {1,2,3} £ A where £ means a belongs to the set X.

Please tell true or false. If false, then explain.

$\large\underline{\bold{ANSWER-}}$

Given that

$\rm :\longmapsto\:A \: = \: \{1,2,3,4,5,6 \}$

Since,

$\rm :\implies\: \{1,2,3 \} \: \subset \: A$

So,

$\bf\implies \: \{1,2,3 \} \: \cancel\in \: A$

$\bf :\longmapsto\:Hence, \: given \: statement \: is \: false.$

Additional Information

Definition of Set :-

• The collection of well-defined distinct objects is known as a set.

• The word well-defined refers to a specific property which makes it easy to identify whether the given object belongs to the set or not.

• The word ‘distinct’ means that the objects of a set must be all different. 

• The objects used to form a set are called its element or its members.

• Generally, the elements of a set are written inside a pair of curly (idle) braces and are represented by commas. The name of the set is always written in capital letter.

Definition of Subset:

• If A and B are two sets, and every element of set A is also an element of set B, then A is called a subset of B and we write it as A ⊆ B or B ⊇. The symbol ⊂ stands for ‘is a subset of’ or ‘is contained in’ 

• Every set is a subset of itself, i.e., A ⊂ A, B ⊂ B. 

• Empty set is a subset of every set.