Question

Given the open sentence n² + 10 = 7n with the replacement set Domain: {1, 3, 5, 7}, what is the solution set?

A) 1
B) 3
C) 5
D) 7

Answer 1

The solution to the open sentence n² + 10 = 7n for the replacement set {1, 3, 5, 7} is found by substitution. Only when n = 5 does the equation hold true, rendering the solution set as {5}.

Step-by-step explanation:

The student is asking to solve the open sentence n² + 10 = 7n for the given replacement set of {1, 3, 5, 7}. To find the solution set, we substitute each value from the domain into the equation and check for which values the equation holds true.

1. For n = 1: 1² + 10 = 7(1) -> 11 = 7, which is false.
2. For n = 3: 3² + 10 = 7(3) -> 19 = 21, which is false.
3. For n = 5: 5² + 10 = 7(5) -> 35 = 35, which is true. Therefore, 5 is part of the solution set.
4. For n = 7: 7² + 10 = 7(7) -> 59 = 49, which is false.

Hence, the solution set for the given open sentence with the replacement set {1, 3, 5, 7} is {5}.