What is Boolean logic?

A system of logic with exactly two values — TRUE and FALSE (or 1 and 0) — used in mathematics, computer science, and electronic circuits Logic that uses the letters A-Z to represent different logical values A type of logic that only applies to yes/no questions The study of how boolean (round) objects move through space

What does the Boolean operator 'AND' mean?

Both conditions must be TRUE for the result to be TRUE — (TRUE AND TRUE) = TRUE, but (TRUE AND FALSE) = FALSE At least one condition must be TRUE for the result to be TRUE Combines two conditions into a list but doesn't evaluate them Both conditions must be FALSE for the result to be TRUE

What does the Boolean operator 'OR' mean?

At least one condition must be TRUE for the result to be TRUE — (TRUE OR FALSE) = TRUE, only (FALSE OR FALSE) = FALSE Exactly one condition (not both) must be TRUE for the result to be TRUE Both conditions must be TRUE for the result to be TRUE Either condition must be FALSE for the result to be TRUE

What does the Boolean operator 'NOT' do?

Reverses a truth value — NOT TRUE = FALSE, NOT FALSE = TRUE Adds a negative number to the result Cancels the previous logical operation Means the condition doesn't apply — it's optional

In a 'knights and knaves' puzzle, what are the rules?

Knights always tell the truth; knaves always lie — every statement can be analyzed knowing this rule to determine who is a knight and who is a knave Knights lie and knaves tell the truth — they're named oppositely to confuse you Knights and knaves both tell the truth but knaves sometimes make mistakes Knights tell the truth during the day; knaves tell the truth at night

Person A says: 'We are both knaves.' What can you conclude?

A is a knave and B is a knight — if A were a knight, A's statement would be true (making A a knave — contradiction), so A must be a knave telling a lie, meaning they are NOT both knaves, so B is a knight Both A and B are knaves — A's statement is true Both A and B are knights — A told the truth about something A is a knight and B is a knave — the opposite of what A claimed

What is a 'truth table'?

A table listing all possible combinations of TRUE/FALSE inputs and the corresponding output for a logical expression — used to analyze and verify logical statements A table of facts that everyone agrees are true, used as a reference A table that lists which statements from various sources are verified as accurate A table comparing what witnesses said versus what actually happened

What is a 'logical contradiction'?

A statement or set of statements that cannot all be true simultaneously — like 'this statement is false' (a self-contradiction), or conclusions that conflict with premises Two people disagreeing about the same fact A statement that is wrong but not logically impossible A paradox that has never been resolved by logicians

What is 'XOR' (exclusive OR) and why is it used in cryptography?

XOR is TRUE when inputs are different and FALSE when they're the same — it's used in encryption because XORing data with a key and then XORing again with the same key perfectly restores the original XOR is the same as OR but only works on numbers, not text XOR is exclusive OR — it means OR but excluding the case where both are true XOR is used to make data bigger so it's harder for attackers to analyze

What is 'proof by contradiction'?

A mathematical proof method where you assume the opposite of what you want to prove, show this leads to a logical contradiction, and conclude the original statement must be true Proving something by finding an example that contradicts it A way to prove your point by contradicting what the other person said Disproven — you can never prove something using contradiction