The word "isolate" means to separate or set apart from others. Now, let's look at the options:
(1) Assuage: This means to relieve or ease something, especially pain or a negative feeling. It is not directly opposite to "isolate" in terms of meaning.
(2) Insulate: To insulate means to protect something by separating it from the surroundings. While it might seem somewhat related, it doesn't directly oppose "isolate," as it still involves separation, but for protection.
(3) Mingle: This means to mix or combine with others. It is the opposite of "isolate" because "mingle" refers to coming together or interacting, whereas "isolate" means to separate.
(4) Transpose: This means to change the order or position of something. It doesn't oppose "isolate" in a meaningful way.
Thus, "mingle" is the word that directly opposes "isolate" since it involves combining or mixing, unlike "isolate," which implies separation.