P-->Q & R-->S: Meaning Explained

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The discussion clarifies the logical implications of the propositions P-->Q and R-->S, where P represents "It is raining" and Q denotes "There are clouds in the sky," while R signifies "giving a cookie by me" and S indicates "cleaning room by kids." The notation "P-->Q" translates to "If P then Q," emphasizing that this does not imply causation in mathematical logic. The distinction between common speech and mathematical logic is crucial, as "P implies Q" does not assert that P causes Q.

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Consider these propositions,

P=It is raining, and Q=There are clouds in the sky
R=giving a cookie by me, and S=cleaning room by kids

What does P-->Q and R-->S mean in words?
 
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phydis said:
Consider these propositions,

P=It is raining, and Q=There are clouds in the sky
R=giving a cookie by me, and S=cleaning room by kids

What does P-->Q and R-->S mean in words?

The notation "P-->Q" for "P implies Q" can also be translated as "If P then Q". Substitute words for the statements represented by "P" and "Q".

But be aware that both "P implies Q" and "If P then Q" have a different meaning in mathematical logic that in common speech. "P implies Q" doesn't assert that "P" causes "Q". The idea of "causation" isn't defined in elementary mathematical logic.
 
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