# Symbolic Logic : Truth Tables

## Example Questions

### Example Question #1 : Symbolic Logic

Looking at the following truth table, find the missing operator if

.

Explanation:

To help solve for the missing operator in this truth table, first recall the different operators and there meanings.

In truth tables when the "or" operator is used translates to, either  and  (the constants) being true. When the "and" operator is used that means that for the result to hold true both the constants must be true. The "not" operator negates the answer. The "implies" that the first constant  results in the second constant . Lastly, the "equivalency" operator signifies that both constants are the same.

Looking at the truth table,

and  result in a true statement whenever the first constant is the same as the second constant. Therefore, the missing operator is "implies".

In mathematical terms the missing operator is .

### Example Question #2 : Truth Tables

Looking at the following truth table, find the missing operator if

.

Explanation:

To help solve for the missing operator in this truth table, first recall the different operators and there meanings.

In truth tables when the "or" operator is used translates to, either  and  (the constants) being true. When the "and" operator is used that means that for the result to hold true both the constants must be true. The "not" operator negates the answer. The "implies" that the first constant  results in the second constant . Lastly, the "equivalency" operator signifies that both constants are the same.

Looking at the truth table,

and  result in a true statement whenever one of the constants is true. Therefore, the missing operator is "or".

In mathematical terms the missing operator is .

### Example Question #3 : Truth Tables

Looking at the following truth table, find the missing operator if

.

Explanation:

To help solve for the missing operator in this truth table, first recall the different operators and there meanings.

In truth tables when the "or" operator is used translates to, either  and  (the constants) being true. When the "and" operator is used that means that for the result to hold true both the constants must be true. The "not" operator negates the answer. The "implies" that the first constant  results in the second constant . Lastly, the "equivalency" operator signifies that both constants are the same.

Looking at the truth table,

The result is always opposite of the value of . Therefore, the missing operator is "not".

In mathematical terms the missing operator is .