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
pq(q ↔ p) → (¬p ↔ q)11?10?01?00?

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

(q ↔ p) → (¬p ↔ q)
N =
2.Easy
ab¬(¬a ∧ (a ∨ ¬b))11100100

Exactly one row of the truth table makes ¬(¬a ∧ (a ∨ ¬b)) false. Click that row.

¬(¬a ∧ (a ∨ ¬b))
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
3.Medium
b → ¬c¬b → ¬c¬b ∧ cb ∧ ¬c

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

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

Which formula is logically equivalent to ¬(q → r)? Click it.

¬(q → r)
  1. 1¬q → ¬r
  2. 2¬q ∨ ¬r
  3. 3q ∧ ¬r
  4. 4q → ¬r
5.Hard
∃x P(x)∀x P(x)∃x ¬P(x)∀x ¬P(x)

Which statement is equivalent to ¬∀x P(x), with the negation moved all the way inside? Click it.

¬∀x P(x)
  1. 1∃x P(x)
  2. 2∀x P(x)
  3. 3∃x ¬P(x)
  4. 4∀x ¬P(x)
6.Hard
¬b → ¬aa → bb ∧ ab → a

The premises b → c; c → a are given. Which conclusion follows from them? Click it.

b → cc → a
  1. 1¬b → ¬a
  2. 2a → b
  3. 3b ∧ a
  4. 4b → a

Answer key

  1. 1. N = 2
  2. 2. a = 0, b = 0
  3. 3. b ∧ ¬c
  4. 4. q ∧ ¬r
  5. 5. ∃x ¬P(x)
  6. 6. b → a

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