The negation of the statement '$7 > 5$ and $8 < 10$' is:

Solution

1. Let $p$ be the statement '$7 > 5$' and $q$ be the statement '$8 < 10$', so the original statement is $p\wedge q$.
2. According to De Morgan's laws, the negation of a conjunction is $\neg (p\wedge q)\equiv \neg p\vee \neg q$.
3. Negating the individual components gives $\neg p$ as '$7\ngtr 5$' and $\neg q$ as '$8\nless 10$'.
4. Combining these with the disjunction operator results in '$7\ngtr 5\vee 8\nless 10$'.
5. Hence the answer is (B).