$1.[6$ marks$]$ Consider each of the following three statements. You can assume for each that $$ is a

set and $$ and $$ are predicates over $.$

Show that each of the statements are not true. You should show this by giving an example of a

situation where they are not equivalent, through providing a specific $($small$,$ non$-$empty$)$ set $$ of

elements and the values $($T$/$F$)$ of the predicates on each element of $.$ You do not have to define

how $$ and $$ work, just what the result of the predicates are on each element of $.$ Be sure to

explain your choices of set and predicate. Remind the reader that duplicati ng this text for the sol ution to their CS $1020$ assig nment is considered a violation of academ ic honesty requirements and would res ult in penalties.

a$.($ in $,())($ in $,(()()))$ implies that $($ in $,(()()))$

b$.$ in $,(()())$ implies that $($ in $,())($ in $,(()())$

c$.($ in $,(()))($ in $,(()))$implies that $$ in $,(()())$