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
pqq ↔ ¬p11?10?01?00?

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

q ↔ ¬p
N =
2.Easy
abc¬(b ↔ (¬c ↔ a))111?110?101?100?011?010?001?000?

Complete the truth table (1 = true, 0 = false). In how many rows N is ¬(b ↔ (¬c ↔ a)) true?

¬(b ↔ (¬c ↔ a))
N =
3.Medium
tautologycontradictioncontingency

Is ¬(c ∧ b) ↔ (¬c ∨ ¬b) a tautology, a contradiction or a contingency? Click your answer.

¬(c ∧ b) ↔ (¬c ∨ ¬b)
  1. 1tautology
  2. 2contradiction
  3. 3contingency
4.Medium
¬(p ∧ q) → ¬r(p ∧ q) ∧ ¬rr → (p ∧ q)¬r → ¬(p ∧ q)

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

(p ∧ q) → r
  1. 1¬(p ∧ q) → ¬r
  2. 2(p ∧ q) ∧ ¬r
  3. 3r → (p ∧ q)
  4. 4¬r → ¬(p ∧ q)
5.Hard
acc ∨ ac¬a11100100

The argument with premises c ∨ a; c and conclusion ¬a is invalid. Click the row of the truth table that is a counterexample.

c ∨ ac∴ ¬a
  1. 1a = 1, c = 1
  2. 2a = 1, c = 0
  3. 3a = 0, c = 1
  4. 4a = 0, c = 0
6.Hard
∃x F(x)∀x F(x)∀x ¬F(x)∃x ¬F(x)

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

¬∃x F(x)
  1. 1∃x F(x)
  2. 2∀x F(x)
  3. 3∀x ¬F(x)
  4. 4∃x ¬F(x)

Answer key

  1. 1. N = 2
  2. 2. N = 4
  3. 3. tautology
  4. 4. ¬r → ¬(p ∧ q)
  5. 5. a = 1, c = 1
  6. 6. ∀x ¬F(x)

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