1. I happened to meet he on the sidewalk.

2. I chanced to meet her on the sidewalk.

3. I met her on the sidewalk by chance.

4. I met her on the sidewalk by accident.

5. I met her on the sidewalk by happen.
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Are they all the same in meaning? What about #5? Is it grammatical?

#5 is not really grammatical...i suppose.Rest of these are approximately same but not actually.

1 is correct IF you mean "her" instead of "he."

2, 3, 4 are correct.

5 is not correct.

The first four sentences have similar meanings, but the fifth one is not grammatically correct. Let's break down each sentence and explain their meanings:

1. "I happened to meet her on the sidewalk": This sentence indicates that meeting her on the sidewalk was a coincidence or by chance.

2. "I chanced to meet her on the sidewalk": This sentence conveys the same meaning as the first sentence, emphasizing that meeting her on the sidewalk was a result of chance or luck.

3. "I met her on the sidewalk by chance": This sentence has the same meaning as the previous two sentences, expressing that meeting her on the sidewalk was not planned but purely accidental.

4. "I met her on the sidewalk by accident": This sentence also implies that the meeting was not intentional but happened unintentionally.

Now, let's address the fifth sentence:

5. "I met her on the sidewalk by happen": This sentence is not grammatically correct. The verb "happen" should be followed by "to" and the base form of a verb (e.g., happen to meet) or by a noun (e.g., happen by chance). Therefore, the correct phrase to use in this case would be "I met her on the sidewalk by happenstance" or "I met her on the sidewalk by chance."