Lectures in Discrete Structures I

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FORMAL LOGIC
Discrete Structures I
FOR-IAN V. SANDOVAL

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Lesson 3
TRUTH TABLES
Source: Google Images

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LESSON OBJECTIVES
❑ Construct truth table for propositional logic

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TRUTH TABLE
1. ~p v ~q
p q
T T
T F
F T
F F

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TRUTH TABLE
1. ~p v ~q
p q ~p
T T F
T F F
F T T
F F T

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TRUTH TABLE
1. ~p v ~q
p q ~p ~q
T T F F
T F F T
F T T F
F F T T

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TRUTH TABLE
1. ~p v ~q
p q ~p ~q ~p v ~q
T T F F F
T F F T T
F T T F T
F F T T T

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TRUTH TABLE
2. p → (p ↔ ~q)
p q
T T
T F
F T
F F

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TRUTH TABLE
2. p → (p ↔ ~q)
p q ~q
T T F
T F T
F T F
F F T

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TRUTH TABLE
2. p → (p ↔ ~q)
p q ~q p ↔ ~q
T T F F
T F T T
F T F T
F F T F

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TRUTH TABLE
2. p → (p ↔ ~q)
p q ~q p ↔ ~q p → (p ↔ ~q)
T T F F F
T F T T T
F T F T T
F F T F T

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TRUTH TABLE
3. p → q ^ (p → ~q)
p q
T T
T F
F T
F F

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TRUTH TABLE
3. p → q ^ (p → ~q)
p q p → q
T T T
T F F
F T T
F F T

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TRUTH TABLE
3. p → q ^ (p → ~q)
p q p → q ~q
T T T F
T F F T
F T T F
F F T T

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TRUTH TABLE
3. p → q ^ (p → ~q)
p q p → q ~q p → ~q
T T T F F
T F F T T
F T T F T
F F T T T

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TRUTH TABLE
3. p → q ^ (p → ~q)
p q p → q ~q p → ~q p → q ^ (p → ~q)
T T T F F F
T F F T T F
F T T F T T
F F T T T T

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r
T T T

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r
T T T
T T F

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r
T T T
T T F
T F T

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r
T T T
T T F
T F T
T F F

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r
T T T
T T F
T F T
T F F
F T T

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r
T T T
T T F
T F T
T F F
F T T
F T F

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r
T T T
T T F
T F T
T F F
F T T
F T F
F F T

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r ~p
T T T F
T T F F
T F T F
T F F F
F T T T
F T F T
F F T T
F F F T

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r ~p ~r
T T T F F
T T F F T
T F T F F
T F F F T
F T T T F
F T F T T
F F T T F
F F F T T

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r ~p ~r q v ~r
T T T F F T
T T F F T T
T F T F F F
T F F F T T
F T T T F T
F T F T T T
F F T T F F
F F F T T T

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TRUTH TABLE
4. ~p ∧ (q v ~r)
p q r ~p ~r q v ~r ~p ∧ (q v ~r)
T T T F F T F
T T F F T T F
T F T F F F F
T F F F T T F
F T T T F T T
F T F T T T T
F F T T F F F
F F F T T T T

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TRUTH TABLES
❑ Enrichment Exercises
Construct the truth table of the following compound
statements.
1. ~p ∧ q
2. (p v q) ∧ ~ (p ∧ q)
3. ~ [(p ∧ q) v ~ (p v q)]
4. (p ↔ ~q) ⊕ (p →q)
5. ~p v (q ∧ ~r)

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• Levin, O. (2019). Discrete Mathematics: An Open Introduction 3rd Edition. Colorado: School of Mathematics Science
University of Colorado.
• Aslam, A. (2016). Proposition in Discrete Mathematics retrieved from https://www.slideshare.net/AdilAslam4/chapter-1-
propositions-in-discrete-mathematics
• Operator Precedence retrieved from http://intrologic.stanford.edu/glossary/operator_precedence.html
REFERENCES