Logic

Negation

Lesson

The negation of a statement $p$ , written $\neg p$ (or “not p”), is the statement with the opposite truth value.

Truth table

  p   | ¬p
 -----+----
   T  |  F
   F  |  T

Double negation

\neg(\neg p) \equiv p

Negating twice gets you back to the original.

How to answer

Use 1 for true and 0 for false.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

p = T. \ \neg p = ?

Problem 2

p = F. \ \neg p = ?

Problem 3

\text{``All triangles have 3 sides.'' is T. } \neg p?

Problem 4

\text{``5 > 10'' is F. } \neg p?

Practice

Standard problems matching the lesson.

Problem 5

\text{``2+2=4'' is T. } \neg p?

Problem 6

\text{``All numbers are even'' is F. } \neg p?

Problem 7

\text{``0 is positive'' is F. } \neg p?

Problem 8

\text{``}\pi\text{ is rational'' is F. } \neg p?

Problem 9

\text{``A triangle has 4 sides'' is F. } \neg p?

Problem 10

\text{``Squares are rectangles'' is T. } \neg p?

Problem 11

\text{``All squares are equal'' is F. } \neg p?

Problem 12

\text{``Even numbers are divisible by 2'' is T. } \neg p?

Problem 13

\text{``1 is prime'' is F. } \neg p?

Problem 14

\text{If } \neg p \text{ is T, what is } p?

Problem 15

\text{If } \neg p \text{ is F, what is } p?

Problem 16

p = T. \ \neg\neg p = ?

Problem 17

p = F. \ \neg\neg p = ?

Problem 18

\text{``10 > 5'' is T. } \neg p?

Challenge

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

Problem 19

\text{``2 is even'' is T. } \neg p?

Problem 20

\neg(\neg(\neg T)) = ?

Problem 21

\neg(\neg(\neg F)) = ?

Problem 22

\neg(T) = ?

Problem 23

\neg(F) = ?

Problem 24

\text{If a statement is true, its negation has truth value?}

Problem 25

\text{The negation of ``no birds fly'' (F)}

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