SURANJAN SAHA and SABITA SAHA Solutions for Chapter: Sets, Exercise 4: EXERCISE-1(IV)

Write down the following statement in set theoretic notation:

$A$ is a subset of $B$.

Write down the following statement in set theoretic notation:

$C$ is a proper subset of $B$.

Write down the following statement in set theoretic notation:

$C$ and $D$ are disjoint sets.

Write down the following statement in set theoretic notation:

$E\text{'}$ is the complement of $E$ in $U$.

If $\mathrm{U}=\left\{\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{o}, \mathrm{u}\right\}$ be the universal set $\mathrm{A}=\left\{\mathrm{a}, \mathrm{i}, \mathrm{u}\right\}$ and $\mathrm{B}=\left\{\mathrm{e}, \mathrm{i},\mathrm{o}\right\}$, Find $\mathrm{A}\text{'}\cup \mathrm{B}\text{'}$

If $\mathrm{U}=\left\{\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{o}, \mathrm{u}\right\}$ be the universal set $\mathrm{A}=\left\{\mathrm{a}, \mathrm{i}, \mathrm{u}\right\}$ and $\mathrm{B}=\left\{\mathrm{e}, \mathrm{i},\mathrm{o}\right\}$, Find $\mathrm{A}\text{'}\cap \mathrm{B}\text{'}$

If $\mathrm{U}=\left\{\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{o}, \mathrm{u}\right\}$ be the universal set $\mathrm{A}=\left\{\mathrm{a}, \mathrm{i}, \mathrm{u}\right\}$ and $\mathrm{B}=\left\{\mathrm{e}, \mathrm{i},\mathrm{o}\right\}$, Find $\left(\mathrm{A}\cup \mathrm{B}\right)\text{'}$

If $\mathrm{U}=\left\{\mathrm{a}, \mathrm{e}, \mathrm{i}, \mathrm{o}, \mathrm{u}\right\}$ be the universal set $\mathrm{A}=\left\{\mathrm{a}, \mathrm{i}, \mathrm{u}\right\}$ and $\mathrm{B}=\left\{\mathrm{e}, \mathrm{i},\mathrm{o}\right\}$. Hence show that $\left(\mathrm{A}\cup \mathrm{B}\right)\text{'}=\mathrm{A}\text{'}\cap \mathrm{B}\text{'}$