Question

Statement I The four conditions $A \subset B, A-B=\phi$, $A \cup B=B$ and $A \cap B=A$ are equivalent.
Statement II If $A \subset B$, then $C-B \not \subset C-A$.

• A. Statement I is true
• B. Statement II is true
• C. Both are true
• D. Both are false

Answer 1

Answer: (A)

Consider the Venn diagram

Here, $A \subset B, A-B=\phi, A \cup B=B$ and $A \cap B=A$
Hence, these four conditions are equivalent.
So, Statement $I$ is true.
Now, let $x \in C-B$
$\Rightarrow x \in C $ and $ x \notin B$
$\Rightarrow x \in C $ and $ x \notin A (\because A \subset B)$
$\Rightarrow x \in C-A$
$\therefore C-B \subset C-A$
Hence, Statement II is not true.