Predicator vs. Predicate

Solution 1:

From the wikipedia article you linked:

This understanding sees predicates as relations or functions over arguments. The predicate serves either to assign a property to a single argument or to relate two or more arguments to each other. Sentences consist of predicates and their arguments (and adjuncts) and are thus predicate-argument structures, whereby a given predicate is seen as linking its arguments into a greater structure.[7]

For example:

• Bob laughed. → laughed (Bob) or, laughed = ƒ(Bob)
• Sam helped you. → helped (Sam, you)
• Jim gave Jill his dog. → gave (Jim, Jill, his dog)

Now for the answer:

Remember that anything which is not an argument, viz...

Other function words - e.g. auxiliary verbs, certain prepositions, phrasal particles, etc. - are viewed as part of the predicate [Wikipedia]

Now,

1. The butter is in the drawer.

This one's easy: is in(the butter, the drawer)

2. You should give it up.

Perhaps your confusion arises from the fact that the words aren't together.

Remember, in certain phrasal verbs (including give up), a pronoun must split the phrase and can't follow the verb.

So, let's have:

2a. You should give up the car.

And, by predicate calculus, we have:

2. should give up (you, it)

2a. should give up (you, the car)

3. Susan is pulling your leg

Now, pulling someone's leg is an idiom that means To make a playful attempt to fool or deceive someone. [TFD]. She isn't literally holding your leg and pulling it. So, leg can't be an argument. (It's not a typo.)

We have: is pulling leg(Susan, your)

However, if it were:

3a. Susan is pulling your hand

We'd have: is pulling(Susan, your hand)

I hope this makes it clear for you. in, up and leg were part of the predicate indeed