LearnTronics
If...Then — Implication
“If this, then that”
Electrical instructions and troubleshooting are full of conditional statements:
If condition A is true, then result B should follow.
The arrow
A → B is read “A implies B” or “if A, then B.”
A useful example outside electronics
If a whole number is divisible by 4, then it is even.
That does not mean that every even number is divisible by 4. The number 6 is the easy counterexample.
The truth table can look odd at first
| A | B | A → B |
|---|---|---|
| F | F | T |
| F | T | T |
| T | F | F |
| T | T | T |
The only false row is the case where A is true but B is false. That is the case where the “if A, then B” promise has actually been broken.
Do not confuse implication with cause
“If A, then B” is a logical relationship. It does not automatically say that A is the physical cause of B, nor does it say that B can happen only because of A.
A little deeper — converse and contrapositive
Original: A → B
Converse: B → A — not automatically equivalent.
Contrapositive: NOT B → NOT A — logically equivalent to the original implication.
This becomes useful in troubleshooting: if a condition really guarantees an outcome, then proving that the outcome is absent can rule out that condition.