$($a$)()$ What constraint does the query $?-$ woman $(x),$ parent $(-,x).$ put on $x,$ i$.$e$.,$ what must $x$ be$,$ given this query?

$($b$)($ What relationship between $x$ and $Y$ does the query

$?-$ parent $(Z,x),$ parent $(Z,Y),\frac{x}{\frac{?}{?}}=Y.$ imply?

Note: that $\frac{\frac{?}{?}}{?}=$ means "not equal to$",$ i$.$e$.,"x$ is not equal to $Y".$

Note: that both of these queries of will produce duplicates $-$ that is okay.

$($a$)1.$ Write an appropriately named rule $($in terms of $x)$ for the query of exercise $2.$a$.$

$($b$)(1,$ Write an appropriately named rule in terms of just $x$ and $Y$ for the query of exercise $2.$b$.$

A note on the meaning of "appropriately named rule" via an example: given the query $?-$ man$(x),$ parent $(x,$dots$).,$ it would follow that $x$ would have to be a father, hence father $(x)$ :$-$ man$(x),$ parent $(x,$dots$).$ would be an appropriately named rule in this case.

Note: again, that your rules may also produce duplicates $-$ that is okay.