Final answer:
The negation of the statement −6 < x < 5 using De Morgan's laws is x ≤ -6 or x ≥ 5. This compound negation combines the negations of x being greater than -6 and x being less than 5.
Step-by-step explanation:
To express the negation of the statement −6 < x < 5 using De Morgan's laws, we want to negate the entire compound inequality. The original statement says x is greater than -6 and less than 5 simultaneously. The negation states that x is either less than or equal to -6 or greater than or equal to 5.
Using De Morgan's laws, the negation of the statement is:
x ≤ -6 or x ≥ 5.
Breaking it down:
Therefore, the compound negation is the combination of both conditions using the word 'or'.