$($Answer must be in $\text{'}V\text{'}$ form a functionally complete collection of logical

$($a$)$ Show that $\text{'}$ not $\text{'}$ and $\text{'}V\text{'}$ form a functionally complete collection of

operators.

$\%$

$"x$ is marks$)$

and $"x$ is beautiful" respectively. Express each of the following statements

using quantifiers, logical connectives, and $T(x),F(x),$ and $B(x).$

$($i$)$ Tigers are fierce.

$($ii$)$ Some tigers are beautiful.

$($iii$)$ Some fierce things are beautiful.

Does $($iii$)$ follow from $($i$)$ and $($ii$)?$ Justify your answer.