Or Truth table
A |
B |
A || B |
| F | F | F |
| F | T | T |
| T | F | T |
| T | T | T |
Not truth table
A |
!A |
| F | T |
| T | F |
Or (written as ||) will result in true if either expression is true and is known as disjunction. Not (written as a !) will negate truth so essentially flips true to false and false to true. Some examples -
Example 1 uses OR to say that if you are under 21 or over 70 then you get a discount rail card.
Example 2 inverts the result of age < 30 so rather than getting people younger than 30 we end up with people older!
Example 3 this negates if we need to take a retake!
We can combine these together in any combination we like to get to the end result. A common end result is known as XOR or exclusive or. The truth table for XOR is -
A |
B |
A XOR B |
| F | F | F |
| F | T | T |
| T | F | T |
| T | T | F |
XOR is only true is one or the other expressions are true but NOT both. In logic we write XOR as -
!(A && B) && (A || B)
A |
B |
A && B | !(A && B) | A || B | !(A && B) && (A || B) |
| F | F | F | T | F | F |
| F | T | F | T | T | T |
| T | F | F | T | T | T |
| T | T | T | F | T | F |
As you can see we get the same truth table. Remember that Java uses &&, || and ! to represent AND, OR and NOT.