We begin by setting the alternating values for the variables.
| (That) logic is easy | only if | everyone studies | but | not everyone studies | implies | logic is not easy. |
| T (logic is easy) | T (everyone studies) | F (everyone studies) | F (logic is easy) | |||
| T | F | T | F | |||
| F | T | F | T | |||
| F | F | T | T |
Next we establish the value of the link for the proposition that sets up the initial relationship between logic being easy and having everyone study.
| (That) logic is easy | only if | everyone studies | but | not everyone studies | implies | logic is not easy. |
| T (logic is easy) | T | T (everyone studies) | F (everyone studies) | F (logic is easy) | ||
| T | F | F | T | F | ||
| F | T | T | F | T | ||
| F | T | F | T | T |
Now we need to see the two premises together. We set the value of the connective expressing their conjunction.
| (That) logic is easy | only if | everyone studies | but | not everyone studies | implies | logic is not easy. |
| T (logic is easy) | T | T (everyone studies) | F | F (everyone studies) | F (logic is easy) | |
| T | F | F | F | T | F | |
| F | T | T | F | F | T | |
| F | T | F | T |
T | T |
The final step is to establish the value of the entire form by deciding the value of the implication. Keep in mind that every valid argument form can be expressed as a conditional, and a conditional (a proposition expressing implication) is false only when the antecedent is true and the consequent is false.
| (That) logic is easy | only if | everyone studies | but | not everyone studies | implies | logic is not easy. |
| T (logic is easy) | T | T (everyone studies) | F | F (everyone studies) | T | F (logic is easy) |
| T | F | F | F | T | T | F |
| F | T | T | F | F | T | T |
| F | T | F | T |
T | T | T |