Question

Consider A = [1, 2] and C = [1, 5). Write down a subset B set. A ⊂ B ⊂ C and A ≠ B and B ≠ C.​

Answer 1

Answer:

B set. A ⊂ B ⊂ C and A ≠ B and B ≠ C.

Answer 2

Answer:

A = {1,2,3} and B = {{1,2,3} ,4,5}

Let’s assume {1,2,3} to be x then,

A = x and B = {x,4,5}

Thus, the entire set A belongs to set B such that set A is a single distinctive element of set B.

Go through the above considerations and definitions thoroughly. Now, wouldn’t you agree that if A ⊂ B then, A ∉ B and when A ∈ B then, A ⊄ B.

If still not clear, let me solve your question.

Given: A, B, and C are three sets. A ∈ B and B ⊂ C

To identify whether A ⊂ C is true or not.

Let’s understand by an example.

Let A = {a} ; B = { {a} , b} ; C = { {a} , b , c} such that A ∈ B and B ⊂ C is not violated.

Let’s denote {a} by x then,

A = x ; B = { x , b} ; C = { x , b , c}

Clearly, A ∈ C and not A ⊂ C. So, A ⊂ C is false.