In each of the following

MATHEMATICS · Subjective · CBSE · Mathematics · Sets · Sets

Problem

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. - If

x \in A

and

A \in B

, then

x \in B

- If

A \subset B

and

B \in C

, then

A \in C

- If

A \subset B

and

B \subset C

, then

A \subset C

- If

A \not\subset B

and

B \not\subset C

, then

A \not\subset C

- If

x \in A

and

A \not\subset B

, then

x \in B

- If

A \subset B

and

x \notin B

, then

x \notin A