True or false with inequalities

Statement

Decide whether each proposition is true or false: (a) $13 \ge 7$; (b) $-4 > -9$; (c) $6 \le 6$; (d) $-3 < -5$.

Solution

Compare each difference with zero:

• (a) $13-7 = 6 > 0$: true.
• (b) $-4-(-9) = 5 > 0$: true.
• (c) $6-6 = 0$, and $\le$ allows equality: true.
• (d) $-3-(-5) = 2 > 0$, so $-3 > -5$: false.