(i) Given,
To find if {3, 4} ⊂ 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,
3 ∈ {3, 4}; however 3∉A
The given statement {3, 4} ⊂ A is incorrect.
(ii) Given that,
\( A = \{1,2,\{3,4\},5\}\)
To find if {3, 4} ∈A is correct or incorrect.
From the above statement,
{3, 4} is an element of A.
{3, 4} ∈A
The given statement is correct.
(iii) Given that,
\( A = \{1,2,\{3,4\},5\}\)
To find if {{3, 4}} ⊂ 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,
{3, 4} ∈ {{3, 4}} and {3, 4} ∈ A
{{3, 4}} ⊂ A
The given statement {{3, 4}} ⊂ A is correct.
(iv) Given that,
\( A = \{1,2,\{3,4\},5\}\)
To find if 1∈ A is correct or incorrect.
From the above statement,
1 is an element of A.
The statement 1∈A is a correct statement.
(v) Given that,
\( A = \{1,2,\{3,4\},5\}\)
To find if 1⊂ 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,
An element of a set can never be a subset of itself. So \( 1\nsubseteq A\)
The given statement 1⊂ A is incorrect statement.
Find the symmetric difference A Δ B, when A = {1, 2, 3} and B = {3, 4, 5}.