> For the complete documentation index, see [llms.txt](https://practical-testing.gitbook.io/home/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://practical-testing.gitbook.io/home/techniques/elementary-comparison.md).
# Elementary Comparison
### Quick Summary
* Elementary Comparison (EC) is similar to a [Decision Table (DT)](/home/techniques/decision-tables-and-trees.md) with binary values (Truth Table).
* Use to:
* Check the effect of each individual condition
* Get a **compact alternative** to a Truth Table.
### AND / OR operators
Condition combinations may be combined using logical AND or OR.
> Example 1: A rule is true if ONE of the conditions is true. This implies OR.\
> (`0/1` are easier to distinguish visually and are therefore used instead of `Y/N` )
>
> \
> \| 0 0 | | 0 |
>
> \| 0 1 | → | 1 |
>
> \| 1 0 | | 1 |
>
> \| 0 1 | | 1 |\
> \
> \
> Example 2: A rule is true only if ALL conditions are true. This implies AND.\
> \
> Notice two things:
>
> * The tables grows exponentially just like a DT: 23= 8 (2 values to the power of 3 conditions)
> * Only ONE compound condition results in the rule being true (last one: `| 1 1 1 |= | 1 |`)
>
> \
> \
> \| 0 0 0 | | 0 |\
> \| 0 0 1 | | 0 |\
> \| 0 1 0 | | 0 |\
> \| 0 1 1 | → | 0 |\
> \| 1 0 0 | | 0 |\
> \| 1 0 1 | | 0 |\
> \| 1 1 0 | | 0 |\
> \| 1 1 1 | | 1 |
Example 2 above illustrates that as long as ONE condition is false, the result remains the same. So instead of exhaustive testing (all 8 combinations), we may **reduce** the number to 4 rules:
* `| 1 1 1 |` - the only scenario with a positive outcome
* `| 0 1 1 |` , `| 1 0 1 |`, `| 1 1 0 |` - where ANY ONE false condition negates the outcome. These tests check the effect of **each individual condition**.
{% hint style="warning" %}
The above allows for reducing the testing effort as part of a calculated risk. There is still a risk that the software logic was written in such a way that e.g. `| 0 0 1 |` causes a bug.
{% endhint %}
### Full DT vs. ET
#### ✅ Full Decision Table (All 8 Combinations)
This covers **all possible combinations** of 3 binary conditions (2³ = 8 rules).
| Rule | Age ≥ 18 | Employed? | Credit Score ≥ 700 | Decision |
|---|
| 1 | Y | Y | Y | Approve |
| 2 | Y | Y | N 🔴 | Reject |
| 3 | Y | N 🔴 | Y | Reject |
| 4 | Y | N | N | Reject |
| 5 | N🔴 | Y | Y | Reject |
| 6 | N | Y | N | Reject |
| 7 | N | N | Y | Reject |
| 8 | N | N | N | Reject |
✂️ Reduced ET Table (Just 4 Rules)\
We pick Rule 1, which leads to the `Approve` decision, and Rules with 🔴 - where a single `N` condition negates the outcome.
| Rule | Age ≥ 18 | Employed? | Credit Score ≥ 700 | Decision |
|---|
| 1 | Y | Y | Y | Approve |
| 2 | Y | Y | N🔴 | Reject |
| 3 | Y | N🔴 | Y | Reject |
| 4 | N🔴 | Y | Y | Reject |