OR in ternary operator, using &&

Using the traditional if statement I can do this:

if(a===0 || b===0) {console.log('aloha amigo')};

But when I try to do something the same thing with a ternary operator, like this:

a===0 || b===0 && console.log('aloha amigo')

I just get errors about unexpected ||.

According to this answer: Precedence: Logical or vs. Ternary operator, we can do it using

condition1 || condition2 ? do if true : do if false

(Sorry I'm not sure how to call the ? : symbols in this case), but I'm not sure how to get it running using && (It means only run the code if returned true).

I created a codepen to test it easily. Here's the whole code:

var a = 0;
var b = 1;

a===0 || b===0 ? console.log('Works here') : console.log('And here');

a===0 || b===0 && console.log('Doesn\'t work here');

a===0 && console.log('The && works for a single test');

Here's the link