Asked by Sofia Mendez on May 10, 2024
Verified
Use a truth table to answer the following question.Which, if any, set of truth values assigned to the atomic sentences shows that the following argument is invalid? C⋅EE⋅C\frac { C \cdot E } { E \cdot C }E⋅CC⋅E
A) C: T E: T
B) C: T E: F
C) C: F E: T
D) C: F E: F
E) None-the argument is valid.
Atomic Sentences
Simple sentences that cannot be broken down into smaller independent parts, typically used to express basic propositions in logic.
Truth Values
Binary labels (true or false) assigned to statements in logic to denote their veracity.
Truth Table
A table used in logic to determine the truthfulness of various combinations of propositions.
- Imbibe the essence of valid arguments.
- Excel in the art of formulating and interpreting truth tables.
- Identify valid and invalid arguments through the utilization of truth values.
Verified Answer
PK
Prashant KumarMay 14, 2024
Final Answer :
E
Explanation :
The argument is valid because the conclusion E⋅CE \cdot CE⋅C follows logically from the premise C⋅EC \cdot EC⋅E in all possible truth assignments. The order of conjunction ( ⋅\cdot⋅ ) does not affect the truth value of the statements; thus, if C⋅EC \cdot EC⋅E is true, then E⋅CE \cdot CE⋅C is also true, and vice versa.
Learning Objectives
- Imbibe the essence of valid arguments.
- Excel in the art of formulating and interpreting truth tables.
- Identify valid and invalid arguments through the utilization of truth values.
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