Lesson 2: Statements and Logic

Section 0 — Warm-up: Statement or Not?

Instructions: Determine if each sentence is a Statement (S) or Not (N). A statement has a clear truth value (true or false). Commands, questions, or expressions with variables are not statements.

1

My battery is below 20%. S N

2

Close the laptop. S N

3

Is the teacher in the room? S N

4

x + 4 = 10 S N

5

Cairo is in Egypt. S N

6

Tomorrow will be sunny. S N

7

Don't run. S N

8

A triangle has 3 sides. S N

9

n is divisible by 3. S N

10

This lesson is interesting. S N

Section 1 — Statement vs Non-statement + Reason

Instructions: Choose the best category for each sentence. A: Statement (has a truth value), B: Command, C: Question, D: Depends on a variable.

11

"7 is an odd number." A B C D

12

"Bring your notebook." A B C D

13

"Is 15 divisible by 5?" A B C D

14

"y − 2 = 6" A B C D

15

"Some birds cannot fly." A B C D

16

"What time does class end?" A B C D

17

"All squares are rectangles." A B C D

18

"x is negative." A B C D

19

"The classroom has a door." A B C D

20

"Turn off the lights." A B C D

21

"2 is even." A B C D

22

"n is prime." A B C D

23

"Please be quiet." A B C D

24

"Is 100 a multiple of 25?" A B C D

25

"a + 1 = 9" A B C D

Section 2 — Fix It: Turn Non-Statements into Statements

Instructions: Rewrite each non-statement as a clear statement that is true or false. For equations with variables, choose a value to make it a statement.

26

"Close the window." → Rewrite as a statement:

27

"x + 5 = 12." → Rewrite by choosing x:

28

"Are you hungry?" → Rewrite as a statement:

29

"n is prime." → Rewrite by choosing n:

30

"Study harder!" → Rewrite as a statement:

31

"y − 2 = 6." → Rewrite by choosing y:

32

"Is the Wi-Fi working?" → Rewrite as a statement:

Section 3A — Propositions: Can it be a proposition?

Instructions: Decide if the sentence can be a proposition (has a truth value). A: Yes, B: No.

33

"The light is on." A B

34

"Do your homework." A B

35

"12 is divisible by 3." A B

36

"x is greater than 5." A B

37

"The test is tomorrow." A B

38

"What is your name?" A B

39

"Some birds can't fly." A B

40

"n is odd." A B

Section 3B — Name the proposition

Instructions: Write each statement as a proposition using p, q, r, etc.

41

Write as a proposition: "A square has 4 sides."

42

Write as a proposition: "17 is prime."

43

Write as a proposition: "This classroom has windows."

44

Write as a proposition: "My bag is heavy."

45

Write as a proposition: "The Wi-Fi is working."

Section 4A — NOT (~): Translate Words → Symbols

Instructions: Translate the sentence into symbols using ~ for "not".

46

Let p: "It is raining." "It is not raining." →

47

Let p: "The light is on." "The light is not on." →

48

Let p: "I studied." "I did not study." →

49

Let p: "The bus is late." "The bus is not late." →

50

Let p: "I have my ID card." "I do not have my ID card." →

Section 4B — NOT (~): Translate Symbols → Words

Instructions: Write ~p in words.

51

Let p: "The phone is charged." ~p in words:

52

Let p: "The door is open." ~p in words:

53

Let p: "I am ready." ~p in words:

Section 5 — Truth Values (fast reasoning)

Instructions: If p is True, then ~p is: (T / F)

54

If p is True, then ~p is: T F

55

If p is False, then ~p is: T F

56

If p = T, then ~p = T F

57

If p = F, then ~p = T F

Section 6A — Truth Tables for NOT

Instructions: Complete the truth table for ~p.

58

When p = T, ~p = T F

59

When p = F, ~p = T F

Section 7 — Real-life interpretation with NOT

Instructions: What does ~p mean in this context?

60

Let p: "I submitted my assignment." ~p means:

A) I submitted my assignment

B) I did not submit my assignment

C) I will submit my assignment

D) Someone submitted the assignment

61

Let p: "The class starts at 8:00." ~p means:

A) The class does not start at 8:00

B) The class starts at 8:00

C) The class starts after 8:00 (always)

D) The class ends at 8:00

Section 8 — Common Mistakes Check

Instructions: Choose the best NOT version.

62

Let p: "The door is open." Which sentence is the best NOT version of p?

A) The door is not open.

B) The door is closed and locked.

C) The door is open wider.

D) The door is opening.

63

Let p: "I passed the quiz." Which is ~p?

A) I didn't pass the quiz.

B) I passed the quiz with a high score.

C) I will pass the quiz.

D) I took the quiz.

Section 9 — Exit Ticket

Instructions: Answer these final questions.

64

Choose the best definition of a statement:

A) any sentence

B) a sentence that is true or false

C) a question

D) a command

65

Is "x + 1 = 4" a statement?

A) Yes

B) No

66

Let p: "The light is on." Write ~p in words:

67

If p = F, then ~p = T F