1-6 Phi
If an argument has false premises, then it is invalid.
FALSE Explanation: Arguments with false premises and a false conclusion can be valid or invalid. Our example is a valid argument with false premises and a false conclusion. Example: All dogs are cats All mice are dogs All mice are cats
If an argument is unsound, then it must be invalid.
False A sound argument has both a valid form and true premises. Unsound arguments can be valid but such arguments will also have false premises. Example: All dogs are cats All mice are dogs All mice are cats
All poodles are dogs
TRUE
Some animals are not dogs
TRUE
Some poodles are dogs
TRUE
The following instance proves that the form is invalid No dogs are cats Some cats are not poodles ∴Some poodles are not dogs
TRUE
All sound arguments have a true conclusion.
TRUE EXPLANATION: A sound argument has both a valid form and true premises. When a valid argument has true premises, then it must have a true conclusion.
All valid arguments with true premises are sound.
TRUE EXPLANATION: The definition of a sound argument is that it has a valid form and true premises. So, all valid arguments with true premises will be sound.
All arguments with true premises and a false conclusion are invalid.
TRUE Explanation: Since a valid argument cannot have even one instance with true premises and a false conclusion, all such arguments are invalid.
Some arguments with false premises and a true conclusion are invalid.
TRUE explanation: Arguments with false premises and a true conclusion may be valid or invalid. Here, we have an example of an invalid argument with false premises and a true conclusion. Example: Some poodles are cats Some dogs are cats Some dogs are poodles
If a valid argument has a false conclusion, then it must be unsound.
TRUE A sound argument has both a valid form and true premises. If a valid argument has a false conclusion, then it must have at least one false premise. Thus, a valid argument with a false conclusion cannot be sound.
According to the Boolean interpretation, the statement 'All unicorns are white' is hypothetical.
TRUE According to the Boolean interpretation, the statement 'All unicorns are white' is hypothetical. This statement does not make a claim of existence. It claims that if there are unicorns, then they are horned animals.
Determine every reason why the folloiwng syllogism is invalid. All M are P No M are S ∴Some S are not P
M is distributed twice. S is distributed once. P is distributed once.
Determine every reason why the following syllogism is invalid All P are M All S are M ∴Some S are not P
M is not distributed. S is distributed once. There is a negative conclusion but no negative premise.
Determine every reason why the following syllogism is invalid Some P are not M All S are M ∴No S are P
P is distributed once
Determine every reason why the following syllogism is invalid. Some M are not P No S are M ∴All S are P
P is distributed once. There are two negative premises but no negative conclusion.
The statement 'All dogs are animals' is hypothetical according to the Boolean interpretation.
True The statement 'All dogs are animals' is hypothetical in Boolean logic because it does not make a claim of existence. This statement claims that if there are dogs, then there are animals. But it does not claim that dogs actually exist.
All arguments with true premises and a true conclusion are sound.
False Response Feedback: A sound argument must have both a valid form and true premises. Invalid arguments can have true premises and a true conclusion. But invalid arguments are unsound. Example: Some poodles are black Some dogs are black . Some dogs are poodles
A singular statement is translated as a universal statement about a one-member class.
True We translate singular statements into categorical statements by rewriting them as universal statements about one-member classes. For example, the statement 'Secretariet is a horse' will be translated as 'All members of the class of Secretariet are horses'. The statement 'Secretariet is not slow' will be translated as 'No member of the class of Secretariet are slow'.
All animals are dogs
FALSE
No poodles are dogs
FALSE
The following instance proves that the form is invalid All dogs are black All cats are black ∴All cats are black
FALSE
The following instance proves that the form is invalid Some dogs are cats No dogs are poodles ∴Some cats are not poodles
FALSE
If an argument is unsound, then it must be invalid.
FALSE EXPLANATION: A sound argument has both a valid form and true premises. Unsound arguments can be valid but such arguments will also have false premises. Example: All dogs are cats All mice are dogs All mice are cats
All arguments with true premises and a true conclusion are sound
FALSE EXPLANATION: A sound argument must have both a valid form and true premises. Invalid arguments can have true premises and a true conclusion. But invalid arguments are unsound.
If an argument is valid and has a true conclusion, then it must be sound.
FALSE EXPLANATION: A valid argument can have false premises and a true conclusion.
If an argument is invalid and the premises are both true, then the conclusion must be false.
FALSE Explanation: An invalid argument form cannot guarantee that the conclusion is true when the premises are true. An invalid argument can have instances where the premises and conclusion are true. Example: Some poodles are black Some dogs are black . Some dogs are poodles
If an argument is valid and has a true conclusion, then it must be sound.
FALSE A valid argument can have false premises and a true conclusion. Example: All cats are dogs All poodles are cats All poodles are dogs
According to the Aristotelian interpretation, the statement 'All unicorns are white' is hypothetical.
FALSE According to the Aristotelian interpretation, all four categorical statements are existential.
An enthymeme is an argument that consists of a universal premise, a singular statement as a premise, and a singular statement as a conclusion.
FALSE An enthymeme is an argument with an unstated premise or conclusion. The missing statement can be inferred from the context of the argument. (A quasi-syllogism has a universal premise, a singular statement as a premise, and a singular statement as a conclusion.)
All arguments that are unsound have false premises.
FALSE An unsound argument can have true premises so long as it is invalid. Example: Some cats are black Some dogs are black Some dogs are cats
The statement 'All unicorns are horned animals' is true according to the Aristotelian interpretation.
FALSE The statement 'All unicorns are horned animals' is false, according to the Aristotelian interpretation. All four categorical statements are existential, according to the Aristotelian interpretation. All four statements make claims of existence. Since unicorns do not exist, the statement 'All unicorns are horned animals' is false.
A valid argument must have a true conclusion.
FALSE EXPLANATION: A valid argument can have a false conclusion but only if it also has at least one false premise. Example: All dogs are cats All mice are dogs All mice are cats
:If an argument is valid and it has false premises, then it must have a false conclusion.
FALSE EXPLANATION: A valid argument with false premises may still have a true conclusion. Example: All cats are dogs All poodles are cats All poodles are dogs
If an argument is sound, then it can be invalid.
FALSE EXPLANATION: By definition, a sound argument has a valid form and true premises. Thus, a sound argument cannot be invalid.
Some valid arguments have true premises and a false conclusion.
FALSE EXPLANATION: By definition, a valid argument cannot have even one instance where the premises are true and the conclusion false. All such arguments are invalid.
If an argument is unsound and it has a false conclusion, then it must have false premises.
FALSE EXPLANATION: If an argument is unsound and the conclusion is false, the argument may still have true premises. In fact, if we have an argument with true premises and a false conclusion, then we know that the argument is invalid (and unsound). Example: Some cats are black Some dogs are black Some dogs are cats
All unsound arguments are invalid.
FALSE EXPLANATION:A sound argument must have both a valid form and true premises. Valid arguments can be unsound; but they will have false premises. Example: All dogs are cats All mice are dogs All mice are cats
All arguments with false premises and a false conclusion are valid.
FALSE Explanation:Arguments with false premises and a false conclusion can be valid or invalid. Our example is an invalid argument with false premises and a false conclusion. Example: Some cats are mice Some dogs are mice Some dogs are cats
If an argument is unsound, then it must have false premises.
FALSE EXPLANATION: An argmuent may be unsound in one of three ways: (1) It may be valid with false premises. (2) It may be invalid with true premises. (3) It may be invalid with false premises. So, some arguments may still be unsound with true premises. These arguments will be invalid. Example: Some poodles are black Some dogs are black Some dogs are poodles
All arguments with false premises and a true conclusion are invalid.
FLASE EXPLANATION: Arguments with false premises and a true conclusion may be valid or invalid. Here, we have an example of a valid argument with false premises and a true conclusion. Example: All cats are dogs All poodles are cats All poodles are dogs
The following instance proves that the form is invalid All dogs are animals. No dogs are cats No cats are animals
TRUE
The following instance proves that the form is invalid All cats are animals All dogs are animals ∴All dogs are cats
TRUE
The statement 'All unicorns are horned animals' is true according to the Boolean interpretation.
TRUE The statement 'All unicorns are horned animals' is true, according to the Boolean interpretation. This statement is hypothetical according to the Boolean interpretation. It does not make a claim of existence. It claims that if there is a unicorn, then it is a horned animal. Since unicorns are defined to be animals with a horn in their forehead, this is true.
The statement 'Some unicorns are horned animals' is existential according to the Boolean interpretation.
TRUE The statement 'Some unicorns are horned animals' is existential according to the Boolean interpretation. This statement makes a claim of existence. It claims that there exists at least one unicorn and it is horned animal. Since unicorns do not exist, this statement is false.
If a valid argument has a false conclusion, then it is unsound.
TRUE EXPLANATION: A sound argument must have both a valid form and true premises. When a valid argument has a false conclusion, it must also have at least one false premise. Thus, a valid argument with a false conclusion will also be unsound.
A sound argument must have a true conclusion
TRUE EXPLANATION:A sound argument, by definition, has a valid form and true premises. When a valid argument has true premises, then it must also have a true conclusion.
Particular statements are existential according to the Boolean interpretation.
True Response Feedback: According to the Boolean interpretation, particular statements are existential. Particular statements make claims of existence. For example, the statement 'Some dogs are black' makes the claim that there exists at least one dog and it is black. The statement 'Some dogs are not black' makes the claim that there exists at least one dog and it is not black.
If an argument is valid and has a true conclusion, then it must be sound.
false Response Feedback: A valid argument can have false premises and a true conclusion. Example:All cats are dogs All poodles are cats All poodles are dogs