Cheatsheet Logic

Boolean operators

"negation" (not \( a \)):

\( a \)\( \lnot a \)
01
10

"and" also known as "conjunction" (\( a \) and \( b \)):

\( a \)\( b \)\( a \land b \)
000
010
100
111

"inclusive or" also known as "disjunction" (\( a \) or \( b \)):

\( a \)\( b \)\( a \lor b \)
000
011
101
111

"exclusive or" (\( a \) xor \( b \)):

\( a \)\( b \)\( a \oplus b \)
000
011
101
110

"implication" (if \( a \), then \( b \)):

\( a \)\( b \)\( a \Rightarrow b \)
001
011
100
111

"iff" also known as "bi-implication" (if and only if \( a \), then \( b \))

\( a \)\( b \)\( a \Leftrightarrow b \)
001
010
100
111