Question 29 \( \begin{array}{l}\text { If you want a loop to quit iterating if } x<10 \text { and } y>3 \\ \text { what would be the proper loop condition test? }\end{array} \) \( \begin{array}{l}(x>10 \| y<3) \\ (x \geq 10 \| y \leq 3) \\ (x<10 \& \& y>3) \\ (x \geq 10 \& \& y \leq 3)\end{array} \)

To determine the proper loop condition that will **quit iterating** when both \( x < 10 \) **and** \( y > 3 \), we need to consider the logical negation of this quitting condition for the loop to continue running. ### Breakdown: 1. **Quitting Condition:** The loop should **exit** when: \[ x < 10 \quad \text{and} \quad y > 3 \] This is represented as: \[ (x < 10 \&\& y > 3) \] 2. **Loop Continuation Condition:** For the loop to **continue** running, the opposite of the quitting condition must be true. Using De Morgan's Law, the negation of the above condition is: \[ \neg(x < 10 \&\& y > 3) \equiv (x \geq 10 \| y \leq 3) \] This means the loop will keep iterating as long as: \[ x \geq 10 \quad \text{or} \quad y \leq 3 \] ### Conclusion: The correct loop condition should ensure the loop continues **unless** \( x < 10 \) **and** \( y > 3 \). Therefore, the proper loop condition test is: \[ (x \geq 10 \| y \leq 3) \] ### **Answer:** \((x \geq 10 \| y \leq 3)\)