1. I set the alarm for 5:30 every morning.

2. I set the alarm clock for 5:30 every morning.

3. I set the alarm to 5:30 every morning.

(Which one is right? Can we use all of them?)

4. The sun is setting in the west.
5. He set the table for dinner.
6. He set the stroke rate.
7. He set a tray down on a table.

(Are the four sentences correct? Do you have some more common expressions in which the verb 'set' is used?)

1 and 2 are best. 3 is awkward.

4 - 7 are all correct.

1 - 3 -- all are correct.

4 - 7 -- all are correct.

Analyze this set of numbers.
My mother used to wash and set her hair every Saturday night.
Please set aside our differences for now.

All of the sentences you provided are grammatically correct and can be used in different contexts. Here's a breakdown of each sentence:

1. "I set the alarm for 5:30 every morning." - This sentence indicates that you are manually adjusting the settings on an alarm to ring at 5:30 every morning.

2. "I set the alarm clock for 5:30 every morning." - This sentence is similar to the first one, but explicitly mentions the alarm clock, emphasizing that you are adjusting the settings on that particular device.

3. "I set the alarm to 5:30 every morning." - This sentence implies that you are setting the time on a pre-existing alarm system rather than manually adjusting the settings.

So, all three sentences are correct and can be used depending on the specific context you are referring to.

Moving on to the second set of sentences:

4. "The sun is setting in the west." - This sentence is correct and simply states that the sun is going down or disappearing below the horizon in the western direction.

5. "He set the table for dinner." - This sentence suggests that someone prepared the table by arranging the necessary items like plates, glasses, cutlery, etc., in anticipation of a dinner event.

6. "He set the stroke rate." - This sentence is a bit ambiguous without further context. However, in a sports or exercise context, it could mean that someone adjusted or established the rate or pace at which the strokes are made, such as in rowing or swimming.

7. "He set a tray down on a table." - This sentence indicates that someone placed a tray on a table, most likely in a careful or deliberate manner.

These four sentences are also correct and demonstrate different ways the verb "set" can be used in common expressions. Here are a few more examples:

- "He set the stage for a grand performance."
- "She set the thermostat to a comfortable temperature."
- "They set a record for the fastest lap time."
- "We need to set a date for the meeting."

Overall, "set" is a versatile verb that can be used in various contexts and expressions.