🔌 逻辑连接词：与、或、非的开关电路🔌 Logical Connectives: AND, OR, NOT as Circuits

上一片里，我们把一句话判成真或假，像一枚硬币只有两面。可生活里的话常常是拼起来的：“带伞并且穿雨衣”“刷卡或者扫码”“不许喧哗”。拼起来之后，整句话是真是假？小算盘机器人接了个新活——帮宝箱管理员装一套开关电路。 Last leaf we judged one plain sentence true or false, like a coin with only two sides. But real sentences are built by joining pieces: “take an umbrella AND wear a raincoat”, “swipe a card OR scan a code”, “do NOT shout”. Once joined, is the whole sentence true? The little abacus robot has a new job — wiring a switch circuit for the treasure-chest keeper.

第 1 步：与 ∧——两把钥匙都拧，宝箱才开Step 1: AND ∧ — both keys must turn

先看最严格的连接词：它要求所有条件都满足。Start with the strictest connective: it demands every condition be met.

机器人把两把钥匙接成一条串联电路，两把都拧灯才亮 — 机器人把两把钥匙接成一条链：钥匙 A、钥匙 B，电流要挨个通过。两个条件都为真，灯才亮、箱才开——这就是「与」（∧，AND），日常话里的“并且”“同时”。比如：插卡 ∧ 输密码 = 取到钱，少任何一步机器都不放行。 The robot chains two keys into one line: key A, then key B — the current must pass through each in turn. Only when both conditions are true does the lamp light and the chest open. That is AND (∧): everyday “and”, “also”, “at the same time”. Insert card ∧ enter PIN = cash out; skip either step and the machine refuses.

那要是两条路都走得通、不用等另一个呢？What if two routes both work — and neither waits for the other?

第 2 步：或 ∨——有一个就行Step 2: OR ∨ — either one will do

串联与并联电路对比：串联两个都闭合才亮，并联一个闭合就亮 — 并联电路给电流留了两条路：A 通、或者 B 通，灯就亮——这就是「或」（∨，OR），日常话里的“或者”“至少一个”。注意：数学的“或”不排他——A、B 都真时整句照样真（两条路都通，灯当然也亮）。例：走前门 ∨ 走后门，都算到家。 A parallel circuit leaves the current two routes: A closed, or B closed, and the lamp lights. That is OR (∨): everyday “or”, “at least one”. Note: maths OR is not exclusive — if A and B are both true, the whole sentence is still true (both routes open, the lamp still shines). Front door ∨ back door — either way, you are home.

最后一位连接词只有一个输入，却把结果整个翻过来。The last connective takes just one input — yet flips the whole result.

第 3 步：非 ¬——把真假反过来Step 3: NOT ¬ — flip true and false

与门、或门、非门三个逻辑门并排 — 「非」（¬，NOT）像一个反向开关：输入真、输出假；输入假、输出真。日常话里的“不”“没有”：¬A =“没插卡”。三位还能合体：电梯能动 = 门关好 ∧ ¬超载。下一片，我们把这些组合的所有情况一次列清楚。 NOT (¬) works like an inverted switch: input true, output false; input false, output true. Everyday “not”, “no”: ¬A = “card not inserted”. The three can team up: lift moves = doors closed ∧ ¬overloaded. Next leaf, we lay out every combination of these expressions — all at once.

🎮 拨开关，配连接词（30 秒）🎮 Flip switches, match connectives (30 seconds)

切换串联 / 并联 / 反向，拨拨开关看灯亮的规律；再把 4 张任务卡配给正确的连接词。Switch between series / parallel / inverted, flip the switches and watch the lamp; then match 4 task cards to the right connectives.

一句话记住它：连接词就是逻辑的“接线方式”：与 = 串联（都要满足），或 = 并联（一个就行），非 = 反着来。 Remember it in one line: connectives are the wiring of logic: AND = series (both), OR = parallel (one is enough), NOT = the other way round.

与 ∧：两个都为真，结果才真——像串联，缺一个就断AND ∧: true only when both are true — like a series circuit, one gap breaks it 或 ∨：有一个为真，结果就真——像并联；两个都真也算真OR ∨: true when at least one is true — like parallel; both true also counts 非 ¬：真变假、假变真——像反向开关，“不”字诀NOT ¬: true becomes false and false becomes true — the inverted switch

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