How can I explain the difference between the denotation and connotation of each word?

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In order to explain the denotation and connotation of any word, you must understand what these terms mean.  Let's first talk about that, and then we can apply the terms to a few examples.  

Denotation is the term we use to refer to a word's definition in the dictionary.  So, for example, if we look up the word "thin," we will find this as one of the definitions:

: not having a lot of extra flesh on the body : not fat (Merriam-Webster)

That is the denotative meaning of the word, exactly what the dictionary says.   

However, there are two ways we arrive at connotative meaning.

The first is by taking note that certain words have an "aura" about them. For example, "slender" is a synonym for "thin," meaning it has the same meaning.  But we tend to use "slender" as a means of saying something good about a person, so its connotative meaning is more "positive" than "thin," even though it means the same thing.  Look at these sentences:

The girl next to me in class is thin.

The girl next to me in class in slender. 

The second sentence is going to give you a prettier picture because of the aura that "slender" has, and you will see a more attractive person in the second sentence than you do in the first sentence. In the first sentence, you will not necessarily see an unattractive girl, but in this context, "thin" is more neutral, not carrying much in the way of connotative meaning. 

The other way connotative meaning is formed is in context. The words around a word can create connotative meaning in a word.  Contrast these statements:

The girl next to me in class is thin.

The girl next to me in class is haggard and thin, with dark circles under her eyes.

Again, the first sentence gives us basically the denotative meaning of "thin," with no particular positive or negative aura.  But in the second statement, because of what else is in the same sentence, the context in which the word "thin" appears, we have a very different picture of what this word means. This is clearly not an attractive, healthy thinness in this girl.  This kind of thin has been given by its context an aura closer to something like "emaciated." 

So, the denotative meaning is what the dictionary says it is.  But connotative meaning comes from the aura the word already has, the meaning beyond what the dictionary tells us or from the words we use with a word to show something beyond the dictionary meaning. 

I do not know what words you are expected to apply these concepts to, but no matter what they are, these are the ways you need to consider them.

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