$3.(10$ points$)$ Consider a relation parent $($X$,$ Y$)$ which means $\text{'}$X$\text{'}$ is a parent of $\text{'}$Y$\text{'}.($a$)(5$ points$)$ Write all the facts $($tuples$)$ that describe the following tree$($b$)(5$ points$)$ Consider the following rules for defining $(,)$:$$ is an ancestor of $$ if $$ is a parent of $.$ is an ancestor of $$ if $$ is a parent of some $,$ and $$ is an ancestor of $.$Write a datalog program and apply it to find all ancestors of all nodes in the above tree.