How to write a bool query of "(A & B) | C" condition in elasticsearch

Following this question: bool query - must and should on same level, what does it means? I wonder how can I achieve a simple logical query in elasticsearch using the bool query: (A & B) | C where A, B, and C are all match queries needed to be combined with bool.

If I understand correctly, the should clause in the bool query only makes those results' scores be higher. If that's the case, how can I achieve an "OR" relation?

Let's say A, B, and C are all number ranges so something like (pseudo code):

(x >= 4 & x<=6) | x=2

From this, I expect to get the potential result set of 2,4,5,6 (="give me all numbers between 4 and 6 inclusive, but 2 is also fine") - but this is not the case since if "&" means "must" - then the "and" and the "or" parts contradict each other (that's what I understood from people who know elasticsearch more than I do).

So maybe I do not understand how the elasticsearch boolean query works, I don't know. A working example that can achieve the above case will be highly appreciated as well.

For example, the following does not work and yields the result set of 4,5,6 only:

{'query': {'bool': {'should': [{'bool': {'must': [{'range': {'x': {'gte': 4}}}, {'range': {'x': {'lte': 6}}}]}}, {'match': {'x': 2}}]}}}

It looks like you did everything right. Try the following.

POST _bulk
{"index":{"_index":"test","_id":"2"}}
{"x":2}
{"index":{"_index":"test","_id":"4"}}
{"x":4}
{"index":{"_index":"test","_id":"5"}}
{"x":5}
{"index":{"_index":"test","_id":"6"}}
{"x":6}
{"index":{"_index":"test","_id":"7"}}
{"x":7}
{"index":{"_index":"test","_id":"8"}}
{"x":8}
{"index":{"_index":"test","_id":"9"}}
{"x":9}
{"index":{"_index":"test","_id":"10"}}
{"x":10}
{"index":{"_index":"test","_id":"11"}}
{"x":11}
{"index":{"_index":"test","_id":"12"}}
{"x":12}

--

POST test/_search
{
  "query": {
    "bool": {
      "should": [
        {
          "bool": {
            "must": [
              {
                "range": {
                  "x": { "gte": 4 }
                }
              },
              {
                "range": {
                  "x": { "lte": 6 }

                }
              }
            ]
          }
        },
        {
          "match": {"x": 2}
        }
      ]
    }
  }
}

output: 4,5,6,2 as expected.