# Truth Table in Discrete Mathematics

#### Joystar1977

##### Active member
Use a truth table to determine that "division into cases" rule of inference is valid.

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
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
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
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
Thank you Evgeny.Makarov!