Let $a, b \in\{0,1\}$. Consider the following statements where $*$ is the $\text{AND}$ operator, $\oplus$ is $\text{EXCLUSIVE-OR,}$ and ${ }^{c}$ denotes the complement function.
- $\max \left\{a * b, b \oplus a^{\mathrm{c}}\right\}=1$
- $\max \left\{a \oplus b, b \oplus a^{\mathrm{c}}\right\}=1$
- $\min \left\{a * b, b * a^{\mathrm{c}}\right\}=0$
- $\min \left\{a \oplus b, b \oplus a^{c}\right\}=1$
Which of the above statements is/are always $\text{TRUE?}$ Choose from the following options.
- $\text{(i)}$ and $\text{(ii)}$ only
- $\text{(ii)}$ and $\text{(iii)}$ only
- $\text{(iii)}$ and $\text{(iv)}$ only
- $\text{(iv)}$ and $\text{(i)}$ only
- None of the above