Final answer:
The inverse of the statement "if Sarah receives the nomination for student cabinet, then she will accept it" is "If Sarah does not receive the nomination for student cabinet, then she will not accept it." To find the inverse, negate both the hypothesis and the conclusion of the original conditional statement.
Step-by-step explanation:
The inverse of the statement, "if Sarah receives the nomination for student cabinet, then she will accept it", is "If Sarah does not receive the nomination for student cabinet, then she will not accept it".
Creating an inverse involves negating both the hypothesis and the conclusion of the original conditional statement. A conditional, or "if-then" statement, establishes a relationship where the occurrence of the second event (the conclusion) is reliant on the occurrence of the first event (the hypothesis). To form an inverse, we negate both parts of the original statement. For example, the inverse of "If it is windy, then my plant will get knocked over" would be "If it is not windy, then my plant will not get knocked over." This exercise is helpful for understanding logic, testing hypotheses, and forming contradictions if we consider combining the original statement with its inverse.