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Logic: fun facts and quiz
The essentials in 7 ideas, with fun facts, an illustrated story and a quiz to see how much you know.
The essentials
Statements
Logic studies what follows from what. It starts with statements that are either true or false, like “7 is an odd number”.
Key fact
A question or a command isn’t a statement: it can’t be true or false.
And, Or, Not
Logic joins statements with AND, OR and NOT. “A AND B” is true only if both are true; “A OR B” is true if at least one is.
Key fact
Computer chips are built from AND, OR and NOT gates.
If… Then
“If it rains, the ground gets wet” doesn’t mean wet ground proves it rained: maybe someone watered the lawn. Flipping an “if” is a classic mistake.
Key fact
This mistake is called “affirming the consequent”.
Syllogisms
A syllogism draws a conclusion from two premises: “All humans are mortal. Socrates is human. So Socrates is mortal.” Aristotle studied them over 2,300 years ago.
Key fact
A valid argument with true premises must have a true conclusion.
Logical Fallacies
A fallacy is a flawed argument that can still sound convincing. Attacking the person instead of their point is called “ad hominem”.
Key fact
A “straw man” twists someone’s argument into a weaker one.
Truth Tables
A truth table lists every combination of true and false inputs, and the result. With two inputs there are four rows; with three, eight.
Key fact
Each extra input doubles the number of rows.
Logic Puzzles
Puzzles like Sudoku are pure logic: no maths needed, just ruling out what can’t be true until only one answer is left.
Key fact
Sudoku’s modern form was created in 1979 by Howard Garns.
Fun facts
Aristotle’s law of the excluded middle says every statement is either true or false, with no third option.
In everyday speech “or” often means one or the other, not both. Logic’s OR allows both; the strict kind is called XOR.
“If it rains, the ground gets wet” means the same as “if the ground is dry, it didn’t rain”. Logicians call that the contrapositive.
Lewis Carroll, author of Alice in Wonderland, taught logic and wrote puzzle books full of silly syllogisms.
The “appeal to nature” fallacy assumes natural means good, yet arsenic and deadly mushrooms are perfectly natural.
Truth tables in their modern form were popularised in the early 1920s, notably by Ludwig Wittgenstein.
The name Sudoku comes from Japanese, roughly “the digits must be single”.
Story: Let Us Calculate!
Let Us Calculate!
1670s. Philosopher Gottfried Leibniz dreams of a language so exact that any argument could be settled like a sum.
Instead of quarrelling, he wrote, two people would just sit down with pens and say to each other: “Let us calculate!”
He never finished it. But his dream fed into modern symbolic logic, and centuries later into the computer.
True or false?
Tap your answer to see if you got it, and why.
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Question 1 of 10
“7 is an odd number” is a true statement.
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True. It’s a claim, and it’s true.
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Question 2 of 10
“A AND B” is true only when both A and B are true.
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True. One false part makes the whole thing false.
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Question 3 of 10
“If A then B” does not mean “if B then A”.
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True. The arrow only points one way.
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Question 4 of 10
Aristotle studied syllogisms.
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True. He was the first to set out formal logic.
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Question 5 of 10
Attacking the person instead of their argument is ad hominem.
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True. Latin for “to the person”.
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Question 6 of 10
A truth table with two inputs has four rows.
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True. TT, TF, FT and FF.
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Question 7 of 10
Sudoku can be solved with logic alone.
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True. The numbers are just symbols: letters would work too.
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Question 8 of 10
“Close the door!” is a statement that can be true or false.
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False. It’s a command, not a claim.
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Question 9 of 10
“A OR B” is false if just one of them is true.
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False. One true part is enough for OR.
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Question 10 of 10
A wet pavement proves that it rained.
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False. Something else could have wet it.
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KnowSoda learns what you know and brings back what you’re about to forget. Logic has 6 more ideas at the Advanced and Expert levels.
