Question

Write the negation of each of the following statements, x as a real number. a)-1 < x < 5​

Answer 1

-1 < x < 5 is x ≤ -1 ∧ x ≥ 5

Explanation:

The given statement is: -1 < x < 5

The negation of this statement is: It is not true that -1 < x < 5.

Alternatively, we can express the negation of the statement by using logical symbols. The symbol "~" means "not", and the symbol "∧" means "and". Therefore, we can write the negation of the statement as:

~(-1 < x < 5)

which is equivalent to:

x ≤ -1 ∧ x ≥ 5

So, the negation of the statement "-1 < x < 5" is "x ≤ -1 ∧ x ≥ 5".