The hypothesis is "the stars are visible".
The conclusion is "it is night".
This is because a conditional follows the format of "if hypothesis, then conclusion". It shortens to "If P, then Q".
It's fairly clear that the original conditional is true. There are some extremely rare exceptions, but mostly stars are only visible at night.
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The converse is "If it is night, then the stars are visible".
Reason: The original "If P, then Q" format flips to "If Q, then P" when forming the converse.
The converse is false. The fact that it is night does not automatically lead to the stars being visible. For example, storm clouds at night can obscure the stars.
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The inverse is "If the stars aren't visible, then it is not night".
We negate both the hypothesis and conclusion. The format of the inverse is "If not P, then not Q".
Like the previous statement, the inverse is false. Why? Because the stars not being visible doesn't automatically mean it's not night. We could have storm clouds covering up the stars. Or perhaps the city has a lot of light pollution to drown out the stars.
The converse and inverse have the same truth value, as they are equivalent statements (just phrased slightly different ways).
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The contrapositive is "If it's not night, then the stars aren't visible".
The original conditional "If P, then Q" leads to the contrapositive "If not Q, then not P". We swap the positions of P and Q. Also, we negate each piece. In a sense, we combine both the inverse and converse operations to get a contrapositive.
The contrapositive is true because "not night" of course means "day", in which the stars aren't present in the sky. The contrapositive and original conditional have the same truth value. The contrapositive is a way to rephrase the original conditional.
Answer:
Hypothesis: "the stars are visible"
Conclusion: "it is night"
Converse: "If it is night, then the stars are visible" - false.
Inverse: "If the stars are not visible, then it is not night." - false.
Contrapositive: "If it is not night, then the stars are not visible" - true.
Step-by-step explanation:
Conditional statement
"If this happens, then that will happen."
Given conditional statement:
Therefore:
Converse statement
The converse of a conditional statement is formed by switching the hypothesis and the conclusion.
Therefore, the converse of the given conditional statement is:
This is a false statement as the stars will not be visible if there is cloud cover at night.
Inverse statement
The inverse of a conditional statement is formed by negating the hypothesis and the conclusion.
Therefore, the inverse of the given conditional statement is:
This is a false statement as the stars will not be visible if there is cloud cover at night.
Contrapositive statement
The contrapositive of a conditional statement is when both the hypothesis and conclusion are negated and then switched.
Therefore, the contrapositive of the given conditional statement is:
It is difficult to say if this is a true or false statement without more information, as it is possible to see bright stars during the daytime through a telescope or a really powerful pair of binoculars.
If we are to assume that "visible" means "visible to the eye" without any magnification assistance, then the statement is true (if we exclude the sun, which is a star).