Question

Statement I The four conditions $A\subset B,A-B=\varphi$, $A\cup B=B$ 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, $A\subset B,A-B=\varphi ,A\cup B=B$ 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.