a$)$ Show that' and $\text{'}$V$\text{'}$ form a functionally complete collection of logical operators.

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$(2$ marks$)$

$($b$)$ Let T$($x$),$ F$($x$),$ and B$($z$)$ be the statements $"$r is a tiger," $"$z is fierce," and $"$r is beautiful," respectively. Express each of the following statements using quantifiers, logical connectives, and T$($r$),$ F$($r$),$ and B$($z$)..$

$($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