Mr Iqbal
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Lesson 3: Connectives and Truth Tables

Work through each section and submit to track progress on this device.

Symbol Key (Same Meaning)

NOT: ¬p is the same as ~p

AND: p ∧ q is the same as p ^ q

OR: p ∨ q is the same as p v q (inclusive OR)

Section A - Re-entry Warm-up: Statement or Not?

Instructions: Decide if each sentence is a statement (S) or not (N).
A statement is definitely True or False. If it depends on an unknown value (like x or n), it is not a statement (yet).
1

"Open the window." S N

2

"7 is a prime number." S N

3

"x is greater than 5." S N

4

"Today is Monday." S N

5

"You must submit the task." S N

6

"The battery is charged." S N

7

"Is the Wi-Fi working?" S N

8

"Bring your notebook tomorrow." S N

9

"n is even." S N

10

"A square has 4 sides." S N

11

"Stop talking." S N

12

"The bus is late." S N

Section B1 - NOT: Words to Symbols

Instructions: Use NOT. You may write ~ or ¬.
13

Let p: "I am late." "I am not late."

14

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

15

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

16

Let p: "The door is open." "The door is not open."

17

Let p: "The battery is charged." "The battery is not charged."

Section B2 - NOT: Symbols to Words

Instructions: Write ~p (or ¬p) in words.
18

Let p: "I have my ID." ~p in words:

19

Let p: "The homework is submitted." ~p in words:

20

Let p: "It is raining." ~p in words:

Section B3 - AND: Words to Symbols

Why this matters: Many school rules need both conditions to be true.
Context: At the school gate, entry is allowed when you have your ID and you are in uniform.
Instructions: Use AND. Write ^.
21

Let p: "I have my ID." Let q: "I am in uniform." Gate rule statement: "I have my ID AND I am in uniform."

22

Scenario: "I do not have my ID AND I am in uniform."

23

Scenario: "I have my ID AND I am not in uniform."

Section B4 - AND: When is it True?

Context: Use the same gate rule where p = "I have my ID" and q = "I am in uniform".
Today: p = True (ID present), q = False (not in uniform). Decide each result.
24

Gate condition p ^ q is: T F

25

Student with no ID but in uniform (~p ^ q) is: T F

26

Student with ID but not in uniform (p ^ ~q) is: T F

Section B5 - OR: Words to Symbols

Why this matters: Some systems allow more than one valid way to complete an action.
Context: At the canteen, payment is accepted by cash or card.
Instructions: Use OR. You may write v or ∨.
Inclusive OR: true when p is true, or q is true, or both.
27

Let p: "I pay cash." Let q: "I pay by card." Accepted payment statement: "I pay cash OR I pay by card."

28

"I do not pay cash OR I pay by card."

29

"I pay cash OR I do not pay by card."

Section B6 - OR Misconception Check

Context: Canteen payment works if p = "pay cash" OR q = "pay by card".
Instructions: In logic, p v q is TRUE when...
30

A) only p is true

B) only q is true

C) p and q are both true

D) A, B, and C are all true

E) only when both are false

Section B7 - Mixed Translation

Why this matters: Tech troubleshooting often combines NOT, AND, and OR in one decision.
Context: p = "The Wi-Fi works." q = "I can submit my homework online."
Instructions: Use only NOT, AND, OR (symbols allowed: ~ ¬ ^ v ∨).
31

"The Wi-Fi does not work AND I can submit my homework online."

32

"The Wi-Fi works OR I cannot submit my homework online."

33

"The Wi-Fi does not work OR I can submit my homework online."

Section C0 - Why are there 4 rows?

Why this matters: Truth tables help you test every possible real situation before applying a rule.
Instructions: Each of p and q can be True or False. How many combinations?
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A) 2

B) 3

C) 4

D) 8

Section C1 - Truth Table Order

Instructions: Choose the correct order of rows for (p, q).
35

A) TT, TF, FT, FF

B) TT, FT, TF, FF

C) TF, TT, FF, FT

D) FF, FT, TF, TT

Section C2 - Truth Table for NOT

Instructions: Complete the truth table for ~p (or ¬p).
p ~p
T
36
F
37

Section C3 - Truth Table for AND

Context: p = "I have my ID", q = "I am in uniform" (gate entry rule).
Instructions: Complete the truth table for p ^ q.
p q p ^ q
T T
38
T F
39
F T
40
F F
41

Section C4 - Truth Table for OR

Context: p = "I pay cash", q = "I pay by card" (either method is accepted).
Instructions: Complete the truth table for p v q (or p ∨ q).
p q p v q
T T
42
T F
43
F T
44
F F
45

Section C5a - Practice: ~q

Let p: "I pay cash." Let q: "I pay by card." (same context as C4)
Real-world statement: "I do not pay by card."
Instructions: Complete the truth table for ~q (or ¬q).
p q ~q
T T
46
T F
47
F T
48
F F
49

Section C5b - Practice: ~p ^ q

Let p: "I pay cash." Let q: "I pay by card." (same context as C4)
Real-world statement: "I do not pay cash AND I pay by card."
Instructions: Fill ~p first, then the final column for ~p ^ q.
p q ~p ~p ^ q
T T
50
54
T F
51
55
F T
52
56
F F
53
57

Section C5c - Practice: p v ~q

Let p: "I pay cash." Let q: "I pay by card." (same context as C4)
Real-world statement: "I pay cash OR I do not pay by card."
Instructions: Fill ~q first, then the final column for p v ~q.
p q ~q p v ~q
T T
58
62
T F
59
63
F T
60
64
F F
61
65

Section C5d - Practice: ~(p ^ q)

Let p: "I pay cash." Let q: "I pay by card." (same context as C4)
Real-world statement: "It is not true that I pay cash AND I pay by card."
Instructions: Fill p ^ q first, then the final column for ~(p ^ q).
p q p ^ q ~(p ^ q)
T T
66
70
T F
67
71
F T
68
72
F F
69
73

Section D (Optional) - Preview: IF–THEN (→) as a Rule

Rule meaning: p → q means “If p happens, then q must happen.”
If p is false (not happening), the rule does not apply.

Rule: If you are in the lab (p), you must wear goggles (q).
74

In lab + goggles: ✅ rule followed ❌ rule broken

75

In lab + NO goggles: ✅ rule followed ❌ rule broken

76

NOT in lab + goggles: ✅ rule not applied ❌ rule broken

77

NOT in lab + NO goggles: ✅ rule not applied ❌ rule broken