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use de morgan's laws to express a negation for the following statement. assume x is a particular real number. −6 < x < 5

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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'.

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