← Logic

Logic

Statements and Truth Values

Lesson

Logic studies statements — declarative sentences that are either true or false, not both. Everything else (questions, commands, exclamations, opinions) is not a statement.

Statements

  • “The sun is hot.” (true)
  • “2 + 2 = 5.” (false — still a statement)
  • “All squares are rectangles.” (true)

Not statements

  • “Close the door.” (command)
  • “Is it raining?” (question)
  • “Wow!” (exclamation)

How to answer

Type 1 if the sentence is a statement, 0 if not.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

“The sun is hot.”\text{``The sun is hot.''}

Problem 2

“Close the door.”\text{``Close the door.''}

Problem 3

“Is it raining?”\text{``Is it raining?''}

Problem 4

“5 + 3 = 8”\text{``5 + 3 = 8''}

Practice

Standard problems matching the lesson.

Problem 5

“2 + 2 = 5”\text{``2 + 2 = 5''}

Problem 6

“What time is it?”\text{``What time is it?''}

Problem 7

“All squares are rectangles.”\text{``All squares are rectangles.''}

Problem 8

“Go to bed.”\text{``Go to bed.''}

Problem 9

“A triangle has 3 sides.”\text{``A triangle has 3 sides.''}

Problem 10

“Wow!”\text{``Wow!''}

Problem 11

“Every prime number is odd.”\text{``Every prime number is odd.''}

Problem 12

“Please be quiet.”\text{``Please be quiet.''}

Problem 13

“The Earth orbits the Sun.”\text{``The Earth orbits the Sun.''}

Problem 14

“Are you hungry?”\text{``Are you hungry?''}

Problem 15

“7 is prime.”\text{``7 is prime.''}

Problem 16

“Look out!”\text{``Look out!''}

Problem 17

“Water freezes at 0∘C.”\text{``Water freezes at } 0^\circ\text{C.''}

Problem 18

“Run faster!”\text{``Run faster!''}

Challenge

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

Problem 19

“If today is Monday, tomorrow is Tuesday.”\text{``If today is Monday, tomorrow is Tuesday.''}

Problem 20

“Solve for x: 2x = 6.”\text{``Solve for x: 2x = 6.''}

Problem 21

“100 is greater than 50.”\text{``100 is greater than 50.''}

Problem 22

“Hello there!”\text{``Hello there!''}

Problem 23

“Some birds cannot fly.”\text{``Some birds cannot fly.''}

Problem 24

“Is 7 prime?”\text{``Is 7 prime?''}

Problem 25

“All even numbers are divisible by 4.”\text{``All even numbers are divisible by 4.''}

Ask the tutor

Stuck on a concept? Want another example? Ask anything about this topic.

Type your own question below, or tap one of the suggestions. The tutor can re-explain the lesson, work through a specific problem with you, generate fresh practice tuned to where you are, or check your reasoning.

Quiz

Test yourself on this topic →

10 questions, no hints. About 5 minutes.