In both of the examples in which that is optional, the relative pronoun is the object of the embedded clause.
Long books [that] religious people like tend to be Bibles. [Religious people like long books.]
Water tanks [that] fish need are spacious. [Fish need water tanks.]
This is also allowed when the relative pronoun is the object of a preposition or another oblique argument of the embedded clause:
This is the boat I escaped in. [I escaped in this boat.]
In your other examples, the relative pronoun is the subject of the embedded clause:
Those that are rotten must be thrown away. [Those are rotten.]
Cars that break down endanger pedestrians. [Cars break down.]
English only allows you to omit that when it has been moved from a non-subject position in the embedded clause, and when it's followed by the subject of the embedded clause. I suspect that the reason for this is the ease of comprehension on the part of the listener. A sentence like Cars break down endanger pedestrians, if it were grammatical, would be extremely hard to parse.
The relative pronoun who(m) refers to animate beings, like people or animals. Personalities, in the meaning it has in your example, means the characteristic traits of a person. A person's personality is not an animate being. You can't take it to the beach, for example, or feed it donuts. The personality of a person is an inanimate object (a thing). The relative pronoun which is used to represent inanimate things.
A defining relative clause gives us extra information which helps the listener to understand which things we are talking about:
- The man who you saw yesterday is my best friend.
Here, who you saw yesterday tells us exactly which man we are talking about. A non-defining relative clause, on the other hand, gives us extra information about something or somebody we can already identify:
- Your father, whom I've known for twenty years, is the most honest man
I've ever met.
Here, the relative clause whom I've known for twenty years, is just giving the listener extra information. It is not helping the listener understand which of her fathers we are talking about!
The relative item that can be used for both things and people/animate beings. However it can only be used in defining relative clauses, and not non-defining ones:
- Your father, that I've known for twenty years, is the most honest man
I've ever met* [wrong]
- The man that you saw yesterday is my best friend. [correct]
- The sandwich that you bought looked very tasty. [correct]
That cannot occur after a preposition that has been moved to the front of the relative clause:
The options for your examples then are:
A Jekyll and Hyde is a person who has two pesonalities, one of which is bad and the other good.
and
He invents a drug which/that can separate them. When he takes the drug, he becomes an evil version of himself, who(m) he calls Mr. Hyde.
Best Answer
Doing Away with One’s Relatives
It appears (that) your test-giver expects you to produce reduced relative clauses here. This is common, but by no means strictly necessary.
The first sentence supports these possible correct solutions:
The first solution above is the most common. the third the least. It is not that your proposed solution two is wrong, only that is less common than solution one is.
The second sentence supports these possible correct solutions, again ranked from most common to least:
Your own proposed solution appears to have a spurious it at the end, which makes no sense here. It is otherwise fine, however.
Relative-pronoun Deletion
What is going on in all these situations is that the relative pronoun (that is) connecting the relative clause to the noun phrase (that) it applies to is usually omissible in English. Another way of saying this is that the zero relative pronoun is often allowed here.
This is perfectly natural and completely common, but it is never obligatory — despite possible protestations to the contrary from your instructor. I’m sure your instructor knows this, so I am guessing (that) this was a test to see whether you knew how to delete relatives if you cared to.
Relative pronouns are who, whom, whose, that, and which. Since we are talking about clauses here, there must be both a subject and verb. The relative pronoun connects its relative clause to the noun phrase (which) the clause modifies.
Object relatives
When the relative pronoun is serving as the object of its clause, as it is here, it can often be safely deleted — and usually is.
Or with a phrase verb:
Note that phrasal verbs can lead to unnatural pied piping, as it does here:
Or using a human/animate subject:
Those are all perfectly fine, and all are encountered often enough in the wild, so to speak.
Subject relatives
When the relative pronoun is serving as the subject of its clause, it is not in general omissible, as this leads to ungrammatical forms unproduced by native speakers:
However, there is one special case that allows for the deletion of the relative pronoun serving as subject: if the verb it governs is a finite inflection of be. In that instance, the relative pronoun and the following be verb are both deleted. This is what linguists refer to as whiz-deletion — which has nothing to do with Gandalf falling into shadow in Moria, even if folks with the whine–wine merger might be momentarily misled. :-)
First, with a prepositional phrase:
Or with a human/animate agent:
Second, with a past participle:
Or with a human/animate agent:
Third, with a present participle:
Or with a human agent:
Whizzers Beware!
Note that whiz deletion can become awkward or even misleading when the relative clause is descriptive instead of restrictive:
My kitten Fluffy, who is always by my pillow when I wake up in the morning, was not there this morning.
My kitten Fluffy, always by my pillow when I wake up in the morning, was not there this morning.
Be careful with whiz deletion in those situations; it may or may not improve the reading.
Another source of trouble from overzealous whiz deletion derives from the participle–gerund duality in English. When there is a present participle involved, whiz deletion can sometimes lead to a misreading. Sometimes this is only on first read, but at other times it is always ambiguous.
This occurs because an -ing verb in English can serve equally well as a participle/adjective as it can a gerund/noun — and if it is a noun, then it can be the head of its own phrase.
It is easy enough to construct a garden path sentence that is misreadable, at least initially:
In the second version, the reader first construes the subject of the sentence to be risk taking, not risk by itself.
The careful writer avoids whiz deletions that imperil clarity, although the mischievous writer may have other goals.
Possessive relatives
No, these are not greedy family members. :) They are relative pronouns that connect their clauses back to the noun phrase in neither a subject nor an object way, but in a possessive way.
These possessive relatives are usually just whose, but may at times be of which instead. There is no difference between those two, though, because whose is not restricted to animate agents (in) the way (that) who and whom are.
One cannot delete possessive relatives at all, because the sentence becomes ungrammatical if one tries.
Compare valid sentences:
With ones rendered invalid once their relatives have been done away with: