Question

Identify the hypothesis and conclusion in the following proposition, and state their truth values. Then determine
whether the entire proposition is true or false.

If London is in England, then Chicago is in Bolivia.


State the hypothesis and conclusion, and give their truth values.


The hypothesis is (1-Chicago is in Bolivia) (2-London in in England)

which is (1-false) (2-true)

the conclusion is (1-Chicago is in Bolivia) (2-London in in England)

Which is (1-false) (2-true)


Is the entire proposition true or false?
O False
O True

Answer 1

Answer:

O False

Step-by-step explanation:

The entire proposition is false because the hypothesis is true (London is in England) but the conclusion is false (Chicago is not in Bolivia). The proposition is an example of  "fallacy of the inverse", when the conclusion of a conditional statement is assumed to be the inverse of the hypothesis, which is not valid reasoning.

Answer 2

Answer:

The hypothesis is (2-London is in England) which is (2-true).

The conclusion is (1-Chicago is in Bolivia) which is (1-false).

The entire proposition is false.

Step-by-step explanation:

A conditional statement is a logical statement that consists of an "if-then" structure, where the "if" part is the hypothesis, and the "then" part is the conclusion.

The given conditional statement is:

• If London is in England, then Chicago is in Bolivia.

The hypothesis appears after "if" and the conclusion appears after "then", so:

• Hypothesis: London is in England
• Conclusion: Chicago is in Bolivia

The truth value of a statement refers to whether the statement is true or false in a given context or under a specific interpretation.

London is the capital city of England. Therefore, as London is in England:

• The hypothesis is true.

Chicago is a city located in the United States, specifically in the state of Illinois. Bolivia, on the other hand, is a country in South America. Therefore, as Chicago is not in Bolivia:

• The conclusion is false.

In a conditional statement, if the hypothesis is true and the conclusion is false, the entire proposition is considered false.