**Puzzle 68**
Define \$$(a, b, c) \leq (a', b', c')\$$ if and only if \$$a \gt a', b \gt b' \, and \, c \lt c'\$$.

**Puzzle 69**
This is a poset since \$$\otimes\$$ is + and + is commutative.

**Puzzle 70**
Define \$$(a, b, c) \leq (a', b', c')\$$ if and only if \$$a \lt a', b \lt b' \, and \, c \gt c'\$$. This is also a poset.