Truth tables can determine which of the following? (Points : 1)
If an argument is valid
If an argument is sound
X If a sentence is valid
All of the above
To determine which options can be determined using truth tables, let's go through each option:
1. "If an argument is valid": Validity refers to whether the conclusion logically follows from the premises in an argument. Truth tables can help determine the validity of an argument by evaluating the truth values of its premises and conclusion. Therefore, truth tables can be used to determine if an argument is valid.
2. "If an argument is sound": Soundness is a higher standard than validity and requires the argument to be both valid and have all true premises. Truth tables alone cannot determine if the premises are true or false, so they cannot determine if an argument is sound. Therefore, truth tables cannot be used to determine if an argument is sound.
3. "If a sentence is valid": A sentence can be considered valid if it is a tautology, meaning it is true for all possible truth value combinations of its variables. Truth tables can be used to determine if a sentence is valid by evaluating its truth values for all possible combinations of its variables. Therefore, truth tables can be used to determine if a sentence is valid.
Based on our analysis, truth tables can determine if an argument is valid and if a sentence is valid. So the correct option is: X If a sentence is valid.