The son of my mother = myself. So the girl's father is the man. Therefore, the girl is his daughter.

These are squares of prime numbers: 2²=4, 3²=9, 5²=25, 7²=49, 11²=121, 13²=169.

Since no reptiles are mammals, and some reptiles are dangerous, then some dangerous things (the dangerous reptiles) are not mammals. Valid conclusion.

All flowers are plants, but only SOME plants are vegetables. We cannot conclude that some flowers are vegetables without knowing if flowers overlap with the vegetables category.

Arranging clockwise: B, A, C, E, D, F. D opposite B (given). A right of B (given). C between A-F, E between D-F. C is opposite to A.

C is mother of A, so C is mother of B. E is father of D, and D is brother of C, so E is father of C. Therefore, E is grandfather of B.

Each letter is shifted forward by 1: T→U, E→F, C→D, H→I, N→O, O→P, L→M, O→P, G→H, Y→Z. Result: UFDIOPHBHZ.

Dancers ⊂ Performers. Some Performers are Artists. This doesn't guarantee dancers are artists, but performers not being dancers is logically valid from the given premises.

M at position 1. P at position 3. Q at position 2 (between M and P). R and S at positions 4 and 5. Either could be rightmost.

Differences: 4, 6, 8, 10, 12. Pattern is n(n+1): 1×2, 2×3, 3×4, 4×5, 5×6, 6×7=42.