1. If you hurry up, you will catch the bus.

2. If you hurry up, you can catch the bus.

3.If you hurry up, you may catch the bus.

4. If you hurry up, you shall catch the bus.

(Are they all grammatical?)

Yes. But 4 is seldom used.

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Yes, all of these sentences are grammatically correct. However, they convey slightly different meanings:

1. "If you hurry up, you will catch the bus." - This sentence implies that catching the bus is very likely if you hurry up.

2. "If you hurry up, you can catch the bus." - This sentence suggests that by hurrying up, it is possible to catch the bus.

3. "If you hurry up, you may catch the bus." - This sentence indicates that there is a chance of catching the bus if you hurry up.

4. "If you hurry up, you shall catch the bus." - This sentence emphasizes the certainty of catching the bus if you hurry up.

Yes, all of these sentences are grammatically correct. They are all different variations of conditional sentences, expressing different levels of possibility or probability. Let me explain each one to you:

1. "If you hurry up, you will catch the bus": This sentence expresses a high level of certainty. It suggests that if you hurry up, it is highly likely that you will catch the bus.

2. "If you hurry up, you can catch the bus": This sentence also expresses a high level of certainty, but with a possibility of choice. It suggests that if you hurry up, it is possible for you to catch the bus if you choose to do so.

3. "If you hurry up, you may catch the bus": This sentence expresses a moderate level of certainty. It suggests that if you hurry up, there is a chance or possibility for you to catch the bus.

4. "If you hurry up, you shall catch the bus": This sentence expresses a strong level of certainty, similar to the first sentence. However, using "shall" instead of "will" can add a sense of obligation or intention.

To summarize, all of the sentences are grammatically correct and convey different levels of certainty or possibility regarding catching the bus.