Through generally indicates transit from one end of something to another (often, but not always, the opposite end). This can involve literal passage through space or time ("We drove through Texas", "I waited through the night"), or figurative movement through a system or process ("Your request is still making its way through the bureaucracy").
By as a preposition has many definitions; the ones that interest us all loosely boil down to "using the means, mechanism, or agency of." If means or mechanism don't sound very different from system or process to you, don't feel bad. These are two of the more difficult prepositions to get right, and sometimes there is no right answer and you just use the one that feels right (or less wrong, anyway). Writers and editors argue over this and related matters all the time.
As a very general rule of thumb, if literal or figurative motion or progression is involved, use through. Otherwise, use by. There are tons of exceptions, however, and sometimes you just use whichever preposition is most conventionally used with the word or phrase, without asking questions.
To look at your examples specifically:
- My house is heated by/through gas. (Gas is the means used to heat your house.)
- I'll pay you by/through check. (A check is the mechanism you use to pay.)
- I learned that by/through a lot of practice. (Practice is a process, and you progressed through it from the point at which you did not possess the skill to the point at which you did.)
- Success only happens by/through hard work. (Hard work is a process, etc.)
- The tickets are available by/through the Internet. ("Through" is a bit of an evolved convention here. Think of the Internet in the popular 1990s-era conception of a virtual realm through which you travel to your destination.)
Those are the easy ones. The other two are harder:
- I'll send it to you by/through mail. (This depends on whether you consider "mail" to be a mechanism or a system. Generally, I would either use by mail or through the mail, with the idea that "mail" is a mechanism, but "the mail" refers to the postal system.)
- Through/by including a warning prompt prior to asking a SA related question, SPAM probes have been thought to isolate workload from the assessment of SA. (ugh, this is just an ugly sentence to begin with; I'd use by including or through the inclusion of, with similar reasoning to the above.)
Both the statements are grammatically and logically right. They depend on their context.
But, the first one seems more logical as you would be viewing the direction from the thrid person angle view. If it was first person angle, then the second would be the appropriate one.
For instance;
1) I went in the opposite direction from the church
2) The office is in the opposite direction to the church.
In (1), it indicates that, you were at the church (First person). And then went to the opposite direction.
In (2), it indicates that, you were not at the church (Third person), but you merely instructed someone about the direction.
Hope this helps.
Best Answer
For this specific scenario, the usage of "opposite to" and "opposite" is indistinguishable in resulting meaning.
However, they cannot be used interchangeably in all cases.
"Opposite" is utilized as an adjective in:
While it is utilized as a preposition in:
The divergence lies in how "opposite" as an adjective can accept an argument before it takes on the prepositional phrase headed by "to" (PP-to).
So while we can say:
We cannot say:
But the following statements tend to be construed in the same manner:
This suggests that the prepositional variant, when contrasted to the adjectival variant, is limited to having the same implied meaning as "opposite in position to". So, in conclusion, "opposite" as the head of the adjectival phrase that dominates PP-to has the potential to be applied with a greater scope.
I think that about covers it.