Total number of participants = 100 Total number of Indian participants = 70 Total number of vegetarian participants = 60 We are asked to verify the two statements:

1. At least 30 Indian participants are vegetarian.

Out of the 100 total participants, 60 are vegetarian. Therefore, there are 60 vegetarian participants in total, and there are 40 non-vegetarian participants ($100 - 60$). There are 70 Indian participants and the number of Indian participants who could be vegetarian ranges from 0 to 60. To find the minimum number of Indian vegetarians, we assume that as many non-Indian participants as possible are vegetarian. If all the 30 non-Indian participants are vegetarian, then the remaining 30 vegetarians must be Indian. So, at least 30 Indian participants are vegetarian. Hence, statement 1 is correct.

2. At least 10 Indian participants are non-vegetarian. There are 70 Indian participants in total, and we already established that at least 30 Indian participants are vegetarian. This means that at most, 40 Indian participants could be non-vegetarian ($70 - 30$). Therefore, there are at least 10 Indian non-vegetarian participants (because $40 - 30 = 10$). Hence, statement 2 is also correct.

Conclusion: Both statements 1 and 2 are correct.