Directions Indicate whether each claim is true or false 1 Al

Directions: Indicate whether each claim is true or false.

1. All sound arguments are valid.

2. If an argument has true premises and a true conclusion, then it must be sound.

3. If two statements are inconsistent, then they must be contradictory.

4. A logical truth and a logical falsehood are contradictory.

5. An argument with a false premise can be sound, so long it’s valid and its conclusion is true.

Translate each of the following claims to LSL. Make sure to provide a complete dictionary.

1. You’ll succeed if you try.

2. Your tv will work only if it’s plugged in.

3. It’s a leap year just in case either it’s a year divisible by four and not by one hundred or it’s a year divisible by 400.

Solution

1) True

A deductive argument is sound if and only if it is both valid, and all of its premises are actually true.

2) False

If an argument is sound, then it is valid and has all true premises. But here, it is not mentioned that all premises are true, hence it may not be valid and hence not a sound even if it has a true conclusion

3) False

if two statements are inconsistent, it does not follow that they must be contradictory to each other. If two statements are contradictory to each other, then they would have opposite truth values in every row of the main columns but if 2 statements are inconsistent then it it is logically possible for both statements to be false.

5) False

A deductive argument is sound if and only if it is both valid, and all of its premises are actually true.