1. No category

Truth Tables for Compound Logical Propositions Worksheet

MAT 17: Introduction to Mathematics
Truth Tables for Compound Logical Statements and Propositions – Answers
Directions:
Complete a truth table for each exercise. Identify any tautologies and equivalent
basic statements (i.e., NOT, AND, OR, IF-THEN, IFF, etc.) where appropriate.
1. (𝑝 ∧ π‘ž) ∨ ~𝑝
𝑝
T
T
F
F
π‘ž
T
F
T
F
π‘βˆ§π‘ž
T
F
F
F
~𝑝
F
F
T
T
(𝑝 ∧ π‘ž ) ∨ ~𝑝
T
F
T
T
Equivalent to 𝑝 β†’ π‘ž
2. ~π‘ž β†’ (~𝑝 ∨ π‘ž)
𝑝
T
T
F
F
π‘ž
T
F
T
F
~π‘ž
F
T
F
T
~𝑝
F
F
T
T
~𝑝 ∨ π‘ž
T
F
T
T
~π‘ž β†’ (~𝑝 ∨ π‘ž )
T
F
T
T
Equivalent to 𝑝 β†’ π‘ž
3. (~𝑝 β†’ π‘ž) ∨ (~𝑝 ∧ ~π‘ž)
𝑝
T
T
F
F
π‘ž
T
F
T
F
~𝑝
F
F
T
T
~𝑝 β†’ π‘ž
T
T
T
F
~π‘ž
F
T
F
T
~𝑝 ∧ ~π‘ž
F
F
F
T
(~𝑝 β†’ π‘ž ) ∨ (~𝑝 ∧ ~π‘ž )
T
T
T
T
Tautology
Prof. Fowler
4. [ 𝑝 ∧ (π‘ž ∨ ~π‘Ÿ) ] β†’ (~𝑝 ∧ π‘ž)
𝑝
T
T
T
T
F
F
F
F
π‘ž
T
T
F
F
T
T
F
F
π‘Ÿ
T
F
T
F
T
F
T
F
~π‘Ÿ
F
T
F
T
F
T
F
T
π‘ž ∨ ~π‘Ÿ
T
T
F
T
T
T
F
T
𝑝 ∧ (π‘ž ∨ ~π‘Ÿ)
T
T
F
T
F
F
F
F
~𝑝
F
F
F
F
T
T
T
T
~𝑝 ∧ π‘ž
F
F
F
F
T
T
F
F
[ 𝑝 ∧ (π‘ž ∨ ~π‘Ÿ) ] β†’ (~𝑝 ∧ π‘ž )
F
F
T
F
T
T
T
T
Prof. Fowler
5. [ (~π‘ž ∧ 𝑝) β†’ π‘Ÿ ] ↔ [ (~π‘Ÿ β†’ ~π‘ž) ∨ 𝑝 ]
𝑝
π‘ž
π‘Ÿ
~π‘ž
~π‘ž ∧ 𝑝
(~π‘ž ∧ 𝑝) β†’ π‘Ÿ
~π‘Ÿ
~π‘Ÿ β†’ ~π‘ž
(~π‘Ÿ β†’ ~π‘ž) ∨ 𝑝
[ (~π‘ž ∧ 𝑝) β†’ π‘Ÿ ] ↔ [ (~π‘Ÿ β†’ ~π‘ž) ∨ 𝑝 ]
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
F
F
T
T
F
F
T
T
F
F
T
T
F
F
F
F
T
T
T
F
T
T
T
T
F
T
F
T
F
T
F
T
T
F
T
T
T
F
T
T
T
T
T
T
T
F
T
T
T
T
T
F
T
F
T
T
Prof. Fowler
6. { π‘Ÿ ∧ [ (~𝑠 ∨ π‘ž) ↔ ~𝑝 ] } β†’ [ ~(~π‘ž ↔ π‘Ÿ) β†’ (𝑠 ∧ ~π‘Ÿ) ]
𝑝
π‘ž
π‘Ÿ
𝑠
~𝑠
~𝑠 ∨ π‘ž
~𝑝
(~𝑠 ∨ π‘ž) ↔ ~𝑝
π‘Ÿ ∧ [ (~𝑠 ∨ π‘ž) ↔ ~𝑝 ]
~π‘ž
~π‘ž ↔ π‘Ÿ
~(~π‘ž ↔ π‘Ÿ)
~π‘Ÿ
𝑠 ∧ ~π‘Ÿ
~(~π‘ž ↔ π‘Ÿ) β†’ (𝑠 ∧ ~π‘Ÿ)
{ π‘Ÿ ∧ [ (~𝑠 ∨ π‘ž) ↔ ~𝑝 ] } β†’
[ ~(~π‘ž ↔ π‘Ÿ) β†’ (𝑠 ∧ ~π‘Ÿ) ]
T
T
T
T
T
T
T
T
F
F
F
F
F
F
F
F
T
T
T
T
F
F
F
F
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
T
F
F
T
T
F
F
T
F
T
F
T
F
T
F
T
F
T
F
T
F
T
F
F
T
F
T
F
T
F
T
F
T
F
T
F
T
F
T
T
T
T
T
F
T
F
T
T
T
T
T
F
T
F
T
F
F
F
F
F
F
F
F
T
T
T
T
T
T
T
T
F
F
F
F
T
F
T
F
T
T
T
T
F
T
F
T
F
F
F
F
T
T
F
F
T
F
T
F
F
T
F
F
F
F
F
F
T
T
T
T
F
F
F
F
T
T
T
T
F
F
T
T
T
T
F
F
F
F
T
T
T
T
F
F
T
T
F
F
F
F
T
T
T
T
F
F
F
F
T
T
F
F
T
T
F
F
T
T
F
F
T
T
F
F
T
T
F
F
T
F
F
F
T
F
F
F
T
F
F
F
T
F
F
F
T
T
T
T
T
F
F
F
T
T
T
T
T
F
T
T
T
T
T
T
T
T
F
T
T
T
T
T
T
T
Prof. Fowler

 Download  Report

Paperzz.com

Your Paperzz

© Copyright 2026 Paperzz