Logic

Conjunction (AND)

Lesson

Conjunction is the logical AND. The compound statement $p \wedge q$ (“p and q”) is true only when BOTH parts are true.

Truth table

  p | q | p∧q
 ---+---+----
  T | T |  T
  T | F |  F
  F | T |  F
  F | F |  F

Use 1 for true, 0 for false.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

T \wedge T

Problem 2

T \wedge F

Problem 3

F \wedge T

Problem 4

F \wedge F

Practice

Standard problems matching the lesson.

Problem 5

T \wedge T \wedge T

Problem 6

T \wedge T \wedge F

Problem 7

\text{``2+2=4 AND 3<5''}

Problem 8

\text{``2+2=4 AND 3>5''}

Problem 9

\text{``5 is even AND 7 is prime''}

Problem 10

\text{``5 is even AND 7 is even''}

Problem 11

\neg T \wedge T

Problem 12

\neg F \wedge T

Problem 13

T \wedge \neg F

Problem 14

F \wedge \neg T

Problem 15

\text{For } p \wedge q \text{ to be T, how many parts must be T?}

Problem 16

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

Problem 17

\text{``A square has 4 sides AND a triangle has 3 sides''}

Problem 18

\text{``A pentagon has 6 sides AND a hexagon has 6 sides''}

Challenge

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

Problem 19

(T \wedge T) \wedge F

Problem 20

(T \wedge F) \wedge T

Problem 21

\neg(T \wedge F)

Problem 22

\neg(T \wedge T)

Problem 23

T \wedge T \wedge T \wedge T

Problem 24

T \wedge T \wedge T \wedge F

Problem 25

\neg(\neg T \wedge \neg F)

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