Question: can every if...then...else statement be converted into an equivalent statement using only ?:

Answer: 
While any use I can think of for the ternary operator can be implemented as an if/else, the converse is not true; at least not without resorting to perverse and pointless 'tricks' that yield no benefit in terms of performance, readability, or maintainability.

The syntax of if/else is:

```
if( <boolean expression> )
    <statment>|<statment block>
else
    <statment>|<statment block>

```

whereas the syntax of the ?: ternary operator is:

```
<boolean expression> ? <expression> : <expression> ;

```

The important thing here being that an `<expression>` and a `<statement>` are different syntactic elements.

The very limited usage of the form:

```
if( b ) x = y else x = z ;

```

can be implemented as:

```
x = b ? y : x ;

```

but here the restriction is that the same variable is being assigned in both the true and false clauses, (and therefore y and z are both at least convertible to the type of x). So it may be said that any *conditional assignment* can be implemented with the ternary operator (after all that is its primary purpose).

Now since a function call is a valid expression, you could wrap the true and false clauses in separate functions, but to do that simply to prove a point is somewhat perverse:

```
if( b )
    true_stuff() ;
else
    false_stuff() ;

```

is equivalent to:

```
b ? true_stuff() : false_stuff() ;

```

and those functions can contain any code at all. 

So to convert the more general if/else case to a ?: operation, the true/false statement blocks must first be wrapped in separate functions. However even then Neil Butterworth's examples will defeat this approach since the behaviour of `break`, `continue`, and `return` affect control flow beyond the confines of the if/else construct, (although perhaps those are also examples of code you want to avoid!). The presence of a `goto` in the if/else would also defeat this approach. .

I think in the end, even if you could, why would you want to?
No.

Both "branches" of the conditional expression must evaluate to the same type, and that type must not be `void`.

For example, you could do this:

```
x > 0 ? printf("Positive!\n") : 0;

```

because `printf` return `int`. (I would only use this in a round of code golf, though; in fact, [I just did](https://stackoverflow.com/questions/2568090/code-golf-word-search-solver/2568590#2568590).)

But you cannot do this:

```
x > 0 ? exit() : 0;

```

because `exit` returns `void` (or, actually, doesn't return at all).