Can you give an inductive definition to define the length of a list L?
In an inductive definition what you have to do is to find a base case and the inductive step.

In your case, suppose to have a list $L$ and let head be the first element and tail the rest of the list.

For example, if $L=[1,2,3,4,5]$:


head = $1$
tail = $[2,3,4,5]$


In order to understand the meaning you could consider writing a recursive function to compute the length of the list.

According to the answer 


Basis: the length of an empty list is 0
Induction: the length of a list is 1+(length of tail(list))


This corresponds to the recursive function

function len(list L)
   if L is empty
        return 0
   else return 1 + len(tail(L))


Same for the second question:

function member(elem x, list L)
   if L is empty
       return false
   if head == x 
       return true
   else return member(x, tail(L))


and this corresponds to say: X is a member of a list L if either


X is the head of the list or
X is a member of the tail of L.