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Home » In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If A ⊂ B and B ⊂ C, then A ⊂ C (ii) If A ⊄ B and B ⊄ C, then A ⊄ C
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If A ⊂ B and B ⊂ C, then A ⊂ C (ii) If A ⊄ B and B ⊄ C, then A ⊄ C
CBSE | Class 11 | Maths | Miscellaneous Exercise | NCERT | Sets
In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. (i) If A ⊂ B and B ⊂ C, then A ⊂ C (ii) If A ⊄ B and B ⊄ C, then A ⊄ C

Solution:

(i) The statement is true

As per the question

A \subset B and B \subset C

Let’s suppose that,

x \in A

Therefore, we have,

x \in B

And x \in C

As a result,

A \subset C

(ii) The statement is false

As per the question

A \notin B

And also,

B \not \subset C

Let’s suppose that,

\begin{array}{l} A=\{1,2\} \\ B=\{0,6,8\} \end{array}

And,

\begin{array}{l} C=\{0,1,2,6,9\} \\ \therefore A \subset C \end{array}

i

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