Cliff is older than Tanya.
Eric is older than Cliff.
If the first two statements are true, then the third statement is:
(A) True
(B) False
(C) Uncertain
(D) Data insufficient
Age Order Analysis
The problem presents three statements about the relative ages of Tanya, Eric, and Cliff. We are given that the first two statements are true and need to determine the truth value of the third statement.
- Statement 1: Tanya is older than Eric. We represent this as $Tanya > Eric$.
- Statement 2: Cliff is older than Tanya. We represent this as $Cliff > Tanya$.
- Statement 3: Eric is older than Cliff. We represent this as $Eric > Cliff$.
We assume Statement 1 and Statement 2 are true.
Deduction from True Statements
By combining the information from the two true statements, we can establish a definitive age order:
Since $Cliff > Tanya$ (Statement 2 is true) and $Tanya > Eric$ (Statement 1 is true), it logically follows that Cliff must be older than Eric.
The combined, true age order is: $Cliff > Tanya > Eric$.
Statement 3 Truth Evaluation
Now, let's evaluate Statement 3: $Eric > Cliff$.
Our deduced order ($Cliff > Tanya > Eric$) clearly shows that Cliff is older than Eric ($Cliff > Eric$).
Therefore, the statement $Eric > Cliff$ contradicts the established true order.
Statement 3 Conclusion
Since Statement 3 contradicts the logical conclusion derived from the first two true statements, Statement 3 must be False.
Important Questions from Logical Inferences
Based on the statements in (1) – (4), which option/s is/are correct?
(1) Thor has a female sibling
(2) Thor has a sister
(3) Thor has visited New Delhi
(4) Thor has visited IndiaIn 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.
When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.
Based only on the above information, which one of the following statements can be logically inferred with certainty?Elvesland is a country that has peculiar beliefs and practices. They express almost all their emotions by gifting flowers. For instance, if anyone gifts a white flower to someone, then it is always taken to be a declaration of one's love for that person. In a similar manner, the gifting of a yellow flower to someone often means that one is angry with that person.
Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty?
(i) In Elvesland, one always declares one's love by gifting a white flower.
(ii) In Elvesland, all emotions are declared by gifting flowers.
(iii) In Elvesland, sometimes one expresses one's anger by gifting a flower that is not yellow.
(iv) In Elvesland, sometimes one expresses one's love by gifting a white flower.
- In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates and they accounted for 60% of the qualified candidates.
Which one of the following is the correct logical inference based on the information provided in the above passage? A duck named Donald Duck says “All ducks always lie."
Based only on the information above, which one of the following statements can be logically inferred with certainty?
