Final answer:
In mathematics, an open sentence is a mathematical equation or inequality with a variable. The replacement set includes possible values for the variable, and the solution set comprises all values from the replacement set that make the open sentence true. Trial and error is a strategy often used to determine the solution set.
Step-by-step explanation:
In mathematics, an open sentence is an equation or inequality that contains a variable. To solve an open sentence, a replacement set is a set of numbers from which possible values for the variable may be chosen. The solution set consists of all values from the replacement set that satisfy the open sentence.
For example, consider the open sentence x+3=7. If the replacement set is {1, 2, 4, 5}, then the solution set is {4} because 4 is the only number from the replacement set that, when substituted for x, makes the open sentence true.
The process of finding the solution set often involves trial and error, where different numbers from the replacement set are substituted into the open sentence until the correct ones are found.