Write statement in symbolic form and construct a truth table.
It is false that Wanda Garner is the president or Judy Ackerman is the treasurer.
In order to write the statement in symbolic form, we need to assign variables to represent the different components of the statement. Let's use the following variables:
P = Wanda Garner is the president
Q = Judy Ackerman is the treasurer
The statement "It is false that Wanda Garner is the president or Judy Ackerman is the treasurer" can be written symbolically as ¬(P ∨ Q).
To construct a truth table, we need to consider all possible combinations of truth values for P and Q. Since we have two variables, there are 2^2 = 4 possible combinations. We can use the following table to organize the truth values:
| P | Q | P ∨ Q | ¬(P ∨ Q) |
|---|---|-------|---------|
| T | T | T | F |
| T | F | T | F |
| F | T | T | F |
| F | F | F | T |
In the table, T represents true and F represents false. The column labeled P ∨ Q represents the value of the logical OR operation between P and Q.
The last column, labeled ¬(P ∨ Q), represents the negation of the previous column. It is obtained by applying the ¬ (negation) operator to each value in the P ∨ Q column.
This truth table shows the possible combinations and the corresponding truth values for the statement ¬(P ∨ Q).