<span>My worst problem is the inability to speak clearly in public. <em>This </em>is not true when I am with my family.</span> The pronoun reference "this" in the sentence is used incorrectly because it used to refer to the whole sentence before it. It implies that the antecedent is "<span>My worst problem is the inability to speak clearly in public."</span> However, the readers don't know which part of that statement "is not true when I am with my family". Is the problem not true? Is the inability to speak clearly in public not true? The antecedent is vague, and we can say that (3) there's no specific antecedent.
Facts and explaining your topic with details
