Final answer:
The negation of the statement "it is not true that x < 7" is the statement "x ≥ 7" which includes 7 and any number greater than 7.
Step-by-step explanation:
When we talk about the negation of a mathematical statement, we are referring to the inverse of the original statement, or simply what must be true if the original statement is false. In this case, we are looking at the statement "it is not true that x < 7" which is a negation itself. To negate this, we must consider what the original statement would be if this negation wasn't there. Thus, the equivalent statement that negates "it is not true that x < 7" is simply "x ≥ 7".
Why is it "x ≥ 7" and not "x > 7"? It's because the original statement encompasses all numbers less than 7. The negation therefore covers all numbers that are not less than 7, which includes 7 itself and any number greater than 7. This understanding can also be correlated to the memoryless property mentioned earlier. For instance, when dealing with probabilities, knowing that an event has not occurred by a certain point (i.e., the event's negation) changes the probabilities of future outcomes, much like the boundary of an inequality changes the set of numbers that satisfy the inequality.