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Truth Table in Discrete Mathematics

Joystar1977

Active member
Jul 24, 2013
119
Use a truth table to determine that "division into cases" rule of inference is valid.
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,504
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.
 

Joystar1977

Active member
Jul 24, 2013
119
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
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,504
What you wrote is a truth table for implication. To repeat,

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.
 

Joystar1977

Active member
Jul 24, 2013
119
Thank you Evgeny.Makarov!