Introduction / Context:
This is a simple chain of inequalities. We compare counts of colored jelly beans. If yellow exceeds red, and red exceeds green, what can we conclude about yellow versus green? The task is to verify whether the given claim is compatible with the premises.
Given Data / Assumptions:
- Let R = number of red beans; G = number of green beans; Y = number of yellow beans.
- Premise 1: R > G.
- Premise 2: Y > R.
- All counts are nonnegative integers.
Concept / Approach:
- Inequality chaining: If Y > R and R > G, then Y > G must hold.
- The claim says Y < G, which contradicts the chained result.
Step-by-Step Solution:
Start from Y > R and R > G.Transitive property of “greater than” gives Y > G.Therefore, “Y is fewer than G” (Y < G) is false.
Verification / Alternative check:
Pick concrete numbers: Let G = 10; then R could be 12 (R > G), and Y could be 15 (Y > R). Indeed, Y > G. No assignment satisfying the premises can make Y < G true.
Why Other Options Are Wrong:
true: Direct contradiction of transitivity.uncertain: The relation is determined; there is no ambiguity.both true and false: A single set of counts cannot satisfy contradictory inequalities.
Common Pitfalls:
Reversing inequality direction when reading multi-step comparisons or overlooking that “more than” chains transitively.
Final Answer:
false
Discussion & Comments