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

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Instead, "P implies Q" and "If P then Q" are just two different ways of saying the same thing, which is that "Q" must be true whenever "P" is true. That is, "P" being true is a sufficient condition for "Q" being true. In summary, P-->Q means "If it is raining, then there are clouds in the sky." Similarly, R-->S means "If I give a cookie, then the kids will clean the room."
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phydis
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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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1. What does the statement "P-->Q & R-->S" mean?

The statement "P-->Q & R-->S" is a logical statement known as a conditional statement. It means that if both P and R are true, then Q and S must also be true. This can also be written as "If P and R, then Q and S."

2. What is the significance of the arrow (--> ) in the statement?

The arrow (--> ) in the statement represents the logical operator "implies". This operator is used to show a logical relationship between two statements, with the first statement being the "antecedent" and the second statement being the "consequent". In this case, the antecedents are P and R, and the consequents are Q and S.

3. Can you give an example of how this statement might be used in a scientific context?

Yes, for example, if we have two hypotheses: "If a plant receives more sunlight (P), then it will grow taller (Q)", and "If a plant receives more nutrients (R), then it will grow taller (S)". We can combine these two hypotheses using the statement "P-->Q & R-->S" to say that if a plant receives both more sunlight and more nutrients, then it will grow taller.

4. What happens if either P or R is false?

If either P or R is false, then the entire statement "P-->Q & R-->S" is considered false. This is because in a conditional statement, if the antecedent is false, then the consequent does not necessarily have to be true.

5. How is this statement different from "P-->Q or R-->S"?

The statement "P-->Q & R-->S" means that both P and R must be true in order for Q and S to be true. On the other hand, the statement "P-->Q or R-->S" means that either P or R can be true, or both can be true, in order for Q and S to be true. This is because the logical operator "or" allows for either statement to be true in order for the statement to be true.

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