determine if deductive or inductive
1. Some mothers are married. Gwen is a mother. Therefore, she is married.
answer: inductive
2. Lady Gaga has no problems. She is a famous singer, and no famous singer has problems
answer: inductive
3. Some Texans are tall. Billy Bob is a Texan. Therefore, Billy Bob is tall.
answer: inductive
Actually, all three examples you provided are deductive reasoning. Deductive reasoning is when you draw conclusions based on general principles or premises. In each case, you are starting with a general statement and applying it to a specific situation.
For example:
1. The general statement is "Some mothers are married." Based on this, you conclude that Gwen, who is a mother, must be married.
2. The general statement is "No famous singer has problems." From this, you conclude that Lady Gaga, who is a famous singer, must not have any problems.
3. The general statement is "Some Texans are tall." From this, you conclude that Billy Bob, who is a Texan, must also be tall.
So, all three examples follow deductive reasoning by applying a general statement to a specific situation.
1. The first argument is actually deductive because it follows the format of a categorical syllogism where the first premise states a universal proposition ("Some mothers are married"), the second premise makes a specific statement related to the first premise ("Gwen is a mother"), and the conclusion logically follows from the premises ("Therefore, she is married"). Therefore, it is deductive.
2. The second argument is also deductive because it follows the format of a categorical syllogism, where the first premise states a universal proposition ("Lady Gaga has no problems"), the second premise makes a specific statement related to the first premise ("She is a famous singer"), and the conclusion logically follows from the premises ("No famous singer has problems"). Therefore, it is deductive.
3. The third argument is, indeed, inductive. It uses the form of a generalization based on a sample, where the first premise states a general statement ("Some Texans are tall"), the second premise makes a specific statement related to the first premise ("Billy Bob is a Texan"), and the conclusion extends the general statement to the specific case ("Therefore, Billy Bob is tall"). However, this argument relies on probability rather than strict logical guarantee.
To determine if a reasoning is deductive or inductive, we need to look at the structure of the argument and the rules of inference being used.
1. Argument: Some mothers are married. Gwen is a mother. Therefore, she is married.
In this argument, the conclusion ("Gwen is married") is not guaranteed based on the premises ("Some mothers are married" and "Gwen is a mother"). Although it may be more likely that Gwen is married since some mothers are married, it is not an absolute certainty. This argument is therefore inductive.
2. Argument: Lady Gaga has no problems. She is a famous singer, and no famous singer has problems.
In this argument, the conclusion ("Lady Gaga has no problems") is based on the premise that "no famous singer has problems." This is a generalization drawn from the premise that Lady Gaga is a famous singer. However, this argument assumes that all famous singers are without problems, which is not necessarily true. This argument is also inductive.
3. Argument: Some Texans are tall. Billy Bob is a Texan. Therefore, Billy Bob is tall.
Similar to the first two arguments, this argument is based on a generalization ("Some Texans are tall") but does not guarantee the truth of the conclusion ("Billy Bob is tall"). It may be more likely that Billy Bob is tall, but it is not certain based solely on these premises. This argument is also inductive.
Inductive reasoning involves drawing general conclusions from specific observations or evidence, but these conclusions are not necessarily always true. Deductive reasoning, on the other hand, involves drawing specific conclusions from general principles or premises, where the conclusion is necessarily true if the premises are true. None of the arguments provided exhibit this deductive structure.