Hello,
Struggling to get my head around this.
So we have this statement.
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If it rains on Monday then mark will carry an umbrella on Monday.
It does not rain on Monday.
You deduce:
Mark does not carry an umbrella on Monday.
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So if we assume that P means it does not rain on Monday.
and Q means Mark doesn't carry an umbrella on Monday.
So we know P>Q and Q is true then its valid? but this doesnt seem right as P is the opposite of the opening suggestion in the statement.
Any help?
P => Q
says nothing about what happens if ~P.
deduction is incorrect
draw Venn diagram
we only know that the rainstorm is in the umbrella circle. He could easily carry the umbrella in a dry northwest breeze.
hypothesis:
If a cow, then a mammal
Converse:
If a mammal, then a cow
(false)
Inverse:
If not a cow, then not a mammal (false)
Contrapositive:
If not a mammal, then not a cow (true)
Hello,
I understand that you are struggling to understand the logical deduction in the given statement. Let's break it down step by step.
The given statement is:
"If it rains on Monday, then Mark will carry an umbrella on Monday."
We can represent this statement using logical symbols as:
P → Q
Where P represents "It rains on Monday" and Q represents "Mark carries an umbrella on Monday."
Now, it is given that "It does not rain on Monday" (which we can represent as ¬P).
Based on this information, we want to deduce the following conclusion:
"Mark does not carry an umbrella on Monday" (which we can represent as ¬Q).
To clarify, you are asking if the deduction ¬P → ¬Q is valid. Let's see how we can determine that using logical reasoning.
In logic, the implication P → Q can be thought of as a conditional statement. It says that if P is true, then Q must be true. However, if P is false, then the statement is still considered true. In other words, the only time when P → Q is false is when P is true and Q is false.
Now, applying this understanding to our deduction ¬P → ¬Q, we need to check if it holds true.
Given that it does not rain on Monday (¬P), we can conclude that the conditional statement P → Q is automatically true since P is false. Therefore, any deduction based on this conditional statement holds true.
In this case, the deduction ¬P → ¬Q is valid because it follows the logic of implication. Since P is false (It does not rain on Monday), it does not affect the truth or falsehood of ¬Q (Mark does not carry an umbrella on Monday).
To summarize, despite P being the opposite of the opening suggestion in the statement, the deduction ¬P → ¬Q is still valid because it follows the rules of logical implication.
I hope this explanation helps clarify the logical deduction in the statement. If you have any further questions, please feel free to ask!