I. Tanya is older than Eric. II. Cliff is older than Tanya. III. Eric is older than Cliff. If the first two statements are true, the third statement is:

Introduction / Context:
This is a simple logical consistency question involving three comparative statements about ages. The task is to assume that the first two statements are true and determine the status of the third statement. Such questions test understanding of transitive relations, in this case the greater than relation for ages, and whether a new statement is compatible with earlier ones.

Given Data / Assumptions:

• Statement I: Tanya is older than Eric.
• Statement II: Cliff is older than Tanya.
• Statement III: Eric is older than Cliff.
• We assume that statements I and II are true and we must classify statement III.

Concept / Approach:
The relation older than is transitive. If A is older than B, and B is older than C, then A is older than C. By translating the statements into an order, we can see whether the third statement fits or contradicts that order. If it directly conflicts, it is certainly false given the premises. If it is compatible in some way, it might be true or uncertain. Here we must carefully track who is older than whom.

Step-by-Step Solution:
Step 1: From statement I, Tanya is older than Eric. Symbolically, T > E.Step 2: From statement II, Cliff is older than Tanya. Symbolically, C > T.Step 3: Combining these, if C > T and T > E, then C is older than both Tanya and Eric. Thus C > T > E.Step 4: This means that in any arrangement where statements I and II are true, Cliff must be the oldest among the three and Eric the youngest.Step 5: Statement III says that Eric is older than Cliff. Symbolically, E > C.Step 6: But our ordering from the first two statements gives C > T > E, which implies C > E, not E > C. Therefore statement III directly contradicts the ordering implied by the first two statements.Step 7: Because this contradiction is unconditional, statement III cannot possibly be true if statements I and II are true. Hence the third statement is certainly false.

Verification / Alternative check: T and T > E. Now check statement III: Eric is older than Cliff would require 20 > 30, which is impossible. No matter what numbers we assign that respect C > T > E, the condition E > C will always fail. This confirms that statement III is necessarily false given the first two statements.

Why Other Options Are Wrong:

• Option A, Certainly true, is wrong because the third statement contradicts the combined order implied by the first two.
• Option C, Cannot be determined, is incorrect because the information is fully sufficient to decide. There is no ambiguity in the relation.
• Option D, None of these, is incorrect because one of the choices, Certainly false, accurately describes the status of statement III.
• Option E mentions a condition about all three being the same age, which is impossible if Tanya is older than Eric and Cliff is older than Tanya.

Common Pitfalls:

• Failing to treat older than as a transitive relation and not combining the first two statements properly.
• Trying to interpret the statements as independent rather than as part of a single ordered comparison.
• Thinking that without specific numbers we cannot decide, even though the relative order is enough.

Final Answer:
If the first two statements are true, then the third statement is certainly false.