Who needs a truth table, when logic operations are at your daily intuition.
I will share you how I have a gut feeling on basic propositional logic operations without remembering it at all. The operations I am talking about are & AND, | OR, → IF…THEN, ↔ IF AND ONLY IF. Since I am a software developer, a strategy gamer, and a sensible guy. It is always an incredibly useful thing.
AND is like mixing things together.
You are about to cook a salad. There are some fresh ingredients(True Values) and some spoiled ingredients(False Values). What would be the result salad if you mix a pair up? — a fresh or spoiled one?
Mixing spoiled food with any food will result in spoiled food anyway. Now you get a “logic identity” as a bonus~ 😁.
OR is like choosing a better thing.
You are about to buy a brand new iPhone XX. You are in an imaginative Apple Store with a piggy wallet to pay. There are 2 identical iPhone XX in front of you. Same memory size, same chips, same color, same material, same everything. Except their pricing, One is inexpensive(True Value). Another is expensive(False Value). What would you choose to buy? — the inexpensive or expersive one.
IF…THEN is like judging a guilty. The interpretation is divided into 3 parts. The front or the actor, the back or the action, and the output or your judgment.
You are about to judge someone. Someone is either an adult neighbor(True Value) or your innocent baby(False Value). He just stares at(True Value) your favorite Van Gogh picture. But one day, he accidentially ruin(False Value) your favorite Van Goh picture. Would you forgive him? — Or not?
↔ IF AND ONLY IF
IF AND ONLY IF is like agreeing.
There is a couple of a husband and his wife. They are discussing what would be the destination for an upcoming vacation. The destination could either be sea(True Value) or the moon(False Value). After an intense individually research, each of them proposes a destination. Will they reach an agreement? — or not?
Maybe your culture, your view is not the same as mine. Feel free to change to anything you comfortable to interpret with. Have a nice logical day. 👋