1. Check V on the item which Tom is happy with.

2. Check a V on the item which Tom is happy with.

3. Check on the item which Tom is satisfied with.

4. Check the box of the item which Tom is dissatisfied with.
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Are they grammatical? Correct them, please.

1. Check the item that Tom is happy with.

2. Tick the item that Tom is happy with.

3. Verify the item that Tom is satisfied with.

4. Mark the box of the item that Tom is dissatisfied with.

The revised sentences are grammatically correct.