Logic

Disjunction (OR)

Lesson

Disjunction is the inclusive OR. $p \vee q$ is true when at least oneof the two is true. It’s only false when both are false.

Truth table

  p | q | p∨q
 ---+---+----
  T | T |  T
  T | F |  T
  F | T |  T
  F | F |  F

Inclusive vs exclusive

Logical OR is inclusive: T∨T is T. Everyday “or” is sometimes exclusive (“coffee or tea” usually means one). Logic uses inclusive OR by default.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

T \vee T

Problem 2

T \vee F

Problem 3

F \vee T

Problem 4

F \vee F

Practice

Standard problems matching the lesson.

Problem 5

T \vee T \vee F

Problem 6

F \vee F \vee F

Problem 7

\text{``2+2=5 OR 3<5''}

Problem 8

\text{``2+2=5 OR 3>5''}

Problem 9

\text{``5 is prime OR 6 is prime''}

Problem 10

\text{``4 is prime OR 6 is prime''}

Problem 11

\neg T \vee T

Problem 12

\neg F \vee F

Problem 13

F \vee \neg T

Problem 14

T \vee \neg F

Problem 15

\text{For } p \vee q \text{ to be F, how many parts must be F?}

Problem 16

\text{For } p \vee q \vee r \text{ to be F, how many parts must be F?}

Problem 17

\text{``A triangle has 4 sides OR a square has 4 sides''}

Problem 18

\text{``5 < 3 OR 7 > 10''}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

(T \vee F) \vee F

Problem 20

(F \vee F) \vee F

Problem 21

\neg(T \vee F)

Problem 22

\neg(F \vee F)

Problem 23

F \vee F \vee F \vee T

Problem 24

(T \wedge F) \vee T

Problem 25

(T \wedge F) \vee F

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