Final answer:
The inverse of a conditional statement p → q is ~p → ~q. This change reflects a shift to a statement where both the hypothesis and the conclusion are negated.
Step-by-step explanation:
The inverse of p → q is → (~p → ~q). In logic, this means that if you start with a conditional statement (if p, then q), the inverse would be (if not p, then not q). The truth value of the original conditional statement and its inverse are not necessarily the same. It's important to differentiate between different forms of logical statements: the inverse, converse, contrapositive, and the original conditional. These forms are distinct even if they may sometimes have the same truth values.
For example, if the original statement is "If it is raining (p), then the ground will be wet (q)," then the inverse is "If it is not raining (~p), then the ground will not be wet (~q)." Here, note that the inverse does not always hold true because the ground might be wet for reasons other than rain, like a sprinkler.
In terms of negative power in algebra, invert a term with a positive exponent, you change it to a negative exponent, placing it in the denominator. Thus, x^-1 is equivalent to 1/x, and this is analogous to finding an inverse in the context of exponents.