MHB Truth Table in Discrete Mathematics

AI Thread Summary
The discussion centers on validating the "division into cases" rule of inference using a truth table. This rule is proposed to derive A ∨ B → C from A → C and B → C. Participants clarify that the truth table must demonstrate that (A → C) ∧ (B → C) → (A ∨ B → C) is a tautology. There is a focus on ensuring the correct construction of the truth table to confirm the rule's validity. The conversation emphasizes the importance of understanding the definitions and implications of validity in logical reasoning.
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Use a truth table to determine that "division into cases" rule of inference is valid.
 
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You'll have to tell us what this rule is and where are you stuck constructing the truth table. My guess is that the rule derives $A\lor B\to C$ from $A\to C$ and $B\to C$, but rule names vary between courses and textbooks. If it is indeed this rule, then you need to construct the truth table for $(A\to C)\land (B\to C)\to(A\lor B\to C)$ and show that it is a tautology.
 
Is this an acceptable truth table in determining that the "division into cases" rule of inference is valid?

p q p arrow q

T T T

T F F

F T T

F F T
 
What you wrote is a truth table for implication. To repeat,

Evgeny.Makarov said:
You'll have to tell us what this rule [i.e., division into cases] is.
Also make sure you know what it means, by definition, for a rule to be valid.

You can put a material that requires alignment inside the [code]...[/code] tags because these tags preserve spaces. E.g.:

Code:
p  q  p -> q
------------
T  T    T
T  F    F
F  T    T
F  F    T

Click on the "Reply With Quote" button to see how this is done.
 
Thank you Evgeny.Makarov!
 
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