And, Or, Not — the Words That Make Rules
Three little words, with exact meanings, that show up everywhere
- › Understand 'and', 'or', and 'not' as precise rules, using everyday examples
- › See why 'or' in logic usually means 'one, the other, or both'
- › Say the exact opposite of a rule correctly (the part everyone gets wrong)
- › Feel how these words connect to how you already make decisions
Words you already use, made exact
Yesterday you saw what it feels like to *know* something is true. Today, three tiny words: and, or, not. You use them constantly — "bring an umbrella if it's raining or cloudy," "you can enter if you have a ticket and you're on the list." Math just pins down their *exact* meaning so there's never any doubt. No formulas again today. Just careful thinking about words you already know.
"And" — both things have to be true
A bouncer at a door has a rule:
> "You get in if you have a ticket AND you're on the list."
When does someone get in? Only when both are true — ticket *and* on the list. Miss either one and you're out. "And" is strict: every part must hold. If your rule has three ands, all three must be true. One failure sinks the whole thing.
ticket? on list? | get in?
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yes yes | YES (both true -> in)
yes no | no (missing the list)
no yes | no (missing the ticket)
no no | no (missing both)That little table just lists every possible situation (each thing is either yes or no, so there are four) and what the rule says in each. Listing all the situations is a superpower: once the table is filled in, there's *nothing left to argue about*. The rule is completely, exactly pinned down.
"Or" — at least one, and here's the surprise
Another rule:
> "Bring an umbrella if it's raining OR it's cloudy."
When do you bring the umbrella? If it's raining. If it's cloudy. And — here's the part that trips people — also if it's both raining *and* cloudy. In everyday speech "or" sometimes means "one or the other but not both" ("soup or salad?"). But in logic and math, "or" almost always means "at least one is true — including both." Only when *neither* is true do you skip the umbrella.
raining? cloudy? | umbrella?
---------------------------------
yes yes | YES (both -> still yes!)
yes no | YES
no yes | YES
no no | no (neither -> skip it)"Not" — flip it
"Not" is the simplest: it flips true to false and false to true. "It is not raining" is true exactly when "it is raining" is false. That's all. But "not" becomes interesting the moment you point it at a whole *rule* — because saying the exact opposite of an and/or rule is where almost everyone slips.
The opposite of a rule (the part people get wrong)
Back to the bouncer: "ticket AND on the list." What's the exact opposite — the situation where you *don't* get in?
The tempting wrong answer is "no ticket AND not on the list." But think: you also fail if you have a ticket but you're *not* on the list. You don't need to be missing *both* to be turned away — missing either one is enough. So the real opposite is:
> "no ticket OR not on the list."
Look what happened: the "and" flipped into an "or", and each part got a "not." That flip is a real rule, and it's worth burning in:
What you did today
You took three words you use every day and made them exact: and needs everything, or needs at least one (both is fine), not flips. And you learned the one move people constantly botch — saying the true opposite of a rule by flipping and/or and negating the parts. That's not "math you memorize"; it's careful thinking you can now trust. Same as the cookies: get concrete, and it's just common sense sharpened.
Say the exact opposite
No formulas, no code — plain words. For each rule below, (a) list all the situations in a little table like the ones above, and (b) write its exact OPPOSITE using the flip rule (and↔or, negate each part), then double-check your opposite makes sense in words: (1) 'You pass the class if you do the homework AND pass the exam.' (2) 'The alarm goes off if a door opens OR a window opens.' (3) 'You get the discount if you're a student OR it's a Tuesday.' Everything you need is in this lesson.
- › For the 'and' rule, your opposite uses 'or' and negates each part
- › For the 'or' rules, your opposite uses 'and' and negates each part
- › You noticed that failing just ONE part of an 'and' rule breaks it
- › Your opposites actually make sense when you read them aloud