Question

Create a Euler diagram to determine whether the syllogism is valid or invalid.

No monkeys eat lizards.
Koko does not eat lizards.
:. Koko is a monkey.

Answer 1

draw a circle label monkeys
draw another circle for things that eat lizards (show it overlapping the first circle by part of it is also outside).
Now Koko could be anywhere in the 2nd circle, so he does not need to be a monkey, but then again he might be. So the conclusion is false.

this follows from the 5th rule necessary for validity of syllogisms, I quote from wikipedia here:
. . . if either premise is negative, the conclusion must also be negative. For similar reasons, no affirmative conclusion about class inclusion can follow if either premise is a negative proposition about class exclusion. A violation results in the fallacy of drawing an affirmative conclusion from negative premises.

Since the 2nd line can be false, implies the conclusion false.