(i) Given that,
A = \(\{1,2,\{3,4\},5\}\)
To find if {1, 2, 5} ⊂ A is correct or incorrect.
A set A is said to be a subset of B if every element of A is also an element of B
A⊂ B if a ∈ A,a ∈ B
From the above statement,
The each element of \( \{1,2,5\}\) is also an element of A, So \( \{1,2,5\}\)⊂ A
The given statement \( \{1,2,5\}\)⊂ A is a correct statement
(ii) Given that,
A = \( \{1,2,\{3,4\},5\}\)
To find if \( \{1,2,5\}∈ A\) A is correct or incorrect.
From the above statement,
Element of \( \{1,2,5\}\) is not an element of A, So \( \{1,2,5\}∉ A\)
So the given statement \( \{1,2,5\}∈ A\) is an incorrect statement.
(iii) Given that,
\( \{1,2,\{3,4\},5\}\)
To find if \( \{1,2,3\}⊂A\) is correct or incorrect.
A set A is said to be a subset of B if every element of A is also an element of B
A⊂ B if a ∈ A,a ∈ B
From the above statement, we notice that,
3 ∈ {1, 2, 3}; where, 3 ∉ A.
\( \{1,2,3\} \nsubseteq A\)
The given statement \( \{1,2,3\}⊂A\) is an incorrect statement.
(iv) Given that,
\( \{1,2,\{3,4\},5\}\)
To find if Φ ∈ A is correct or incorrect.
A set A is said to be a subset of B if every element of A is also an element of B
A⊂ B if a ∈ A,a ∈ B
From the above statement,
Φ is not an element of A. So, Φ ∈ A.
The given statement Φ ∈ A is an incorrect statement.
(v) Given that,
\( \{1,2,\{3,4\},5\}\)
To find if Φ ⊂ A is correct or incorrect
A set A is said to be a subset of B if every element of A is also an element of B
A⊂ B if a ∈ A,a ∈ B
From the above statement,
Since Φ is a subset of every set, Φ ⊂ A
The given statement Φ ⊂ A is a correct statement.
(vi) Given that,
\( \{1,2,\{3,4\},5\}\)
To find if {Φ} ⊂ A is correct or incorrect.
A set A is said to be a subset of B if every element of A is also an element of B
A⊂ B if a ∈ A,a ∈ B
From the above statement,
Φ is an element of A and it is not a subset of A.
The given statement {Φ} ⊂ A is an incorrect statement.
Answered by Abhisek | 1 year agoFind the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.