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 tigers can run, then tigers have flippers.

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

the hypothesis is tigers can run, which is true. the conclusion is tigers have flippers, which is false.

is the entire proposition true or false?
true
false

Explanation:

Identify hypothesis and conclusion

Using the Hypothesis and Conclusion knowledge point

• The conditional statement is: "If tigers can run, then tigers have flippers."
• The hypothesis \(p\) is the clause following "If": "tigers can run".
• The conclusion \(q\) is the clause following "then": "tigers have flippers".

Determine individual truth values

Using the Truth Values knowledge point

• Hypothesis \(p\) ("tigers can run"): Tigers are indeed capable of running, so this statement is true.
• Conclusion \(q\) ("tigers have flippers"): Tigers do not have flippers (they have paws), so this statement is false.

Evaluate the conditional statement

Using the Conditional Statements knowledge point

• A conditional statement \(p

ightarrow q\) is false only when a true hypothesis leads to a false conclusion.

• Since the hypothesis is true and the conclusion is false, the entire proposition is false.

Answer:

The hypothesis is <blank>tigers can run</blank>, which is <blank>true</blank>. The conclusion is <blank>tigers have flippers</blank>, which is <blank>false</blank>.

Is the entire proposition true or false?

• True
• False (Correct answer)