Asked by Abdul Aleem Chilwan on May 10, 2024
Verified
Prove the following claim:
If at least one member of a set of statements is self-contradictory,
then the set of statements is inconsistent.
Self-Contradictory
A statement or proposition that contradicts itself or is logically inconsistent.
Inconsistent
Describes a condition of being in conflict, having statements or beliefs that cannot all be true at the same time.
- Establish the correctness of logical statements linked with conjunctions, conditionals, and consistency within sets.
Verified Answer
JC
James ContehMay 15, 2024
Final Answer :
Suppose a member of a set of statements is self-contradictory.Hence, that statement is false for every combination of truth values of its atomic components.So, there is no combination of truth values on which all the members of the set of statements is true.Therefore, the set of statements is inconsistent.
Learning Objectives
- Establish the correctness of logical statements linked with conjunctions, conditionals, and consistency within sets.