Propositional logic & proofs worksheet with answers

Free printable Propositional logic & proofs worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
pqr(q → r) ∧ (p ∧ q)111?110?101?100?011?010?001?000?

Complete the truth table (1 = true, 0 = false). In how many rows N is (q → r) ∧ (p ∧ q) true?

(q → r) ∧ (p ∧ q)
N =
2.Easy
pq¬(¬p ∧ (q ↔ p))11100100

Exactly one row of the truth table makes ¬(¬p ∧ (q ↔ p)) false. Click that row.

¬(¬p ∧ (q ↔ p))
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
3.Medium
¬b ∧ ¬c¬b ∨ c¬b ∨ ¬c¬b ∧ c

Which formula is logically equivalent to ¬(b ∧ c)? Click it.

¬(b ∧ c)
  1. 1¬b ∧ ¬c
  2. 2¬b ∨ c
  3. 3¬b ∨ ¬c
  4. 4¬b ∧ c
4.Medium
¬p → ¬(r ∧ q)p ∧ ¬(r ∧ q)(r ∧ q) → p¬(r ∧ q) → ¬p

You want to prove p → (r ∧ q) by contrapositive. Which implication do you prove instead? Click it.

p → (r ∧ q)
  1. 1¬p → ¬(r ∧ q)
  2. 2p ∧ ¬(r ∧ q)
  3. 3(r ∧ q) → p
  4. 4¬(r ∧ q) → ¬p
5.Hard

How many of the 16 rows of the truth table make (p ∧ (r ∨ ¬s)) ∧ (¬(¬p ∨ q) ↔ s) true? Call this number N.

(p ∧ (r ∨ ¬s)) ∧ (¬(¬p ∨ q) ↔ s)
N =
6.Hard

How many of the 16 rows of the truth table make ((¬d ∧ c) ∨ b) ↔ (a ↔ ¬(b ∧ d)) true? Call this number N.

((¬d ∧ c) ∨ b) ↔ (a ↔ ¬(b ∧ d))
N =

Answer key

  1. 1. N = 1
  2. 2. p = 0, q = 0
  3. 3. ¬b ∨ ¬c
  4. 4. ¬(r ∧ q) → ¬p
  5. 5. N = 3
  6. 6. N = 8

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