If you are turning in a truth table, your grader needs to be able to read it. Consider the following truth table:
Truth tables: What not to do.
If you are turning in a truth table, your grader needs to be able to read it. Consider the following truth table:
ABC Aà(B&C) Cà~B Av~A Cà(~A&B) ~Bà(A&C) Cà~C
TTT T T T T T T F T T T F T F F F T F T T T T T F
F/TTF T F F T F T F F TT F TFF TF TTTF TF
TTF/ T F F T F TF F T T F F T FF T F T T T F T F
F
TFT
TFF
FTT
FTF
FFT
FFF
I am not going to bother to finish the table. But I will ask this question. Can you read this table easily? Do you know which statement letter or connective the truth values fall under? If not, then YOU SHOULD NOT TURN IN SOMETHING LIKE THIS. If your grader needs to spend more than 10 minutes to read your table, you deserve to earn 0 points for your table.
Also, do not do this:
Aà(B&C) Cà~B Av~A Cà(~A&B) ~Bà(A&C) Cà~C
T F T F T F
F T T T T T
F T T F T F
F T T T F T
T F T T T F
T T T T T T
T T T F F F
T T T T F T
So, what’s wrong with this? This is certainly readable. The problem is that your reader does not know how you set up your initial conditions. Suppose your initial conditions are these.
ABC
TTT
TTF
TFT
TFF
FTT
FTF
FFT
FFF
If this is how you set up your initial conditions, then your truth table is correct. But suppose you had B or C in the first column, then your table is incorrect. So, what should you do? Give the reader a bit more information. This is fine:
ABC Aà(B&C) Cà~B Av~A Cà(~A&B) ~Bà(A&C) Cà~C
TTT T F T F T F
TTF F T T T T T
TFT F T T F T F
TFF F T T T F T
FTT T F T T T F
FTF T T T T T T
FFT T T T F F F
FFF T T T T F T
If you provide a table such as this and your table is correct, there is no problem. But suppose you make a mistake. It is easy to make a typo when you type up a truth table. The problem is that your grader does not know whether you made a “dumb” mistake or a real mistake. There is not enough information to figure out whether the mistake was a typo or due to a misunderstanding of the material.
It is also fine to construct your truth table in an actual table. And it is fine to split it up. This is also fine.
| A | B | C | A | à | (B | & | C) | C | à | ~B | A | v | ~A | |||
| T | T | T | T | T | T | T | T | T | F | F | T | T | F | |||
| T | T | F | T | F | T | F | F | F | T | F | T | T | F | |||
| T | F | T | T | F | F | F | T | T | T | T | T | T | F | |||
| T | F | F | T | F | F | F | F | F | T | T | T | T | F | |||
| F | T | T | F | T | T | T | T | T | F | F | F | T | T | |||
| F | T | F | F | T | T | F | F | F | T | F | F | T | T | |||
| F | F | T | F | T | F | F | T | T | T | T | F | T | T | |||
| F | F | F | F | T | F | F | F | F | T | T | F | T | T |
| C | à | (~A | & | B) | ~B | à | (A | & | C) | C | à | ~C | ||
| T | F | F | F | T | F | T | T | T | T | T | F | F | ||
| F | T | F | F | T | F | T | T | F | F | F | T | T | ||
| T | F | F | F | F | T | T | T | T | T | T | F | F | ||
| F | T | F | F | F | T | F | T | F | F | F | T | T | ||
| T | T | T | T | T | F | T | F | F | T | T | F | F | ||
| F | F | T | T | T | F | T | F | F | F | F | T | T | ||
| T | F | T | F | F | T | F | F | F | T | T | F | F | ||
| F | T | T | F | F | T | F | F | F | F | F | T | T |
This is not two tables. It is still one table. But it makes it easier to handle. And this way if you make a mistake, it makes it easier for your grader to see if you just made a “dumb” mistake or a typo or whether you just did not know what you’re doing.
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