For each of the following statements, determine whether the statement is true or false. If the statement is true, give
two specific examples that illustrate the statement. If it is false, give a specific counterexample.
(a) If a < b, then a + c < b + c.
(b) If a < b, then ac < bc.
(c) If Person X knows Person Y and Person Y knows Person Z, then Person X knows Person Z.

(a) If a < b, then a + c < b + c is true. This rule holds for all real numbers because adding the same value to both sides of an inequality preserves the inequality.Example:If a = 2 and b = 5, and c = 3, then2 + 3 = 5 and 5 + 3 = 8 → 5 < 8 ✅Another example:a = -1, b = 0, c = 10 → -1 + 10 = 9, 0 + 10 = 10 → 9 < 10 ✅(b) If a < b, then ac < bc is false. This only holds if c is positive. If c is negative, it reverses the inequality.Counterexample:Let a = 2, b = 4, and c = -1.Then ac = 2 × (-1) = -2 and bc = 4 × (-1) = -4.But -2 < -4 is false, because -2 is greater than -4 ❌(c) If Person X knows Person Y and Person Y knows Person Z, then Person X knows Person Z is false."Knowing" is not always a transitive relationship.Counterexample:Person X knows their teacher (Y), and the teacher knows the principal (Z), but it doesn’t mean Person X knows the principal ❌Let me know if you need more help! If this helps, feel free to mark it Brainliest

Answered by ulancheskadana | 2025-07-09

ASSUMING THAT ALL VARIABLES ARE NON NEGATIVEAnswer:TRUETRUEFALSEStep-by-step explanation:12< 15 THEN 12+3 < 15+312 < 15 THEN 12 X 3 < 15 X 3

Answered by czhann | 2025-07-09