A contradiction arises when a proposition is false in every imaginable situation. (Kroeger, 2019, p. 37) Contradictions may also arise in entailment when it is impossible for one statement to be true and another to also be true.
The below example demonstrates that the truth conditions for the first portion of the statement require that the speaker has done an action resulting in the killing of the bear, meaning that it should be dead. However, in stating that it didn’t die, the speaker has contradicted themself since killing typically results in death. Therefore, it is impossible for both of these statements to be true, resulting in a contradiction.
Jacobs, P. W. (2011). Control in Skwxwu7mesh. [Doctoral dissertation, The University of British Columbia].
Kroeger, P. R. (2019). Analyzing meaning: An introduction to semantics and pragmatics. Language Science Press.