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
pqp ∨ (q ↔ ¬p)11?10?01?00?

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

p ∨ (q ↔ ¬p)
N =
2.Easy

How many rows N does the complete truth table of ¬((c → ¬a) ↔ c) ∧ (¬a ∧ b) have?

¬((c → ¬a) ↔ c) ∧ (¬a ∧ b)
N =
3.Medium
(q ∨ r) ∧ p(q ∧ r) ∨ (q ∧ p)(q ∨ r) ∧ (q ∨ p)q ∧ (r ∨ p)

Which formula is logically equivalent to q ∨ (r ∧ p)? Click it.

q ∨ (r ∧ p)
  1. 1(q ∨ r) ∧ p
  2. 2(q ∧ r) ∨ (q ∧ p)
  3. 3(q ∨ r) ∧ (q ∨ p)
  4. 4q ∧ (r ∨ p)
4.Medium
p ∧ ¬q¬p ↔ ¬q¬p ∨ ¬qp ↔ ¬q

Which formula is logically equivalent to ¬(p ↔ q)? Click it.

¬(p ↔ q)
  1. 1p ∧ ¬q
  2. 2¬p ↔ ¬q
  3. 3¬p ∨ ¬q
  4. 4p ↔ ¬q
5.Hard
∀x ¬A(x)∃x ¬A(x)∀x A(x)∃x A(x)

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

¬∀x A(x)
  1. 1∀x ¬A(x)
  2. 2∃x ¬A(x)
  3. 3∀x A(x)
  4. 4∃x A(x)
6.Hard
r ∧ ¬p¬rp¬p

The premises r → p; r are given. Which conclusion follows from them? Click it.

r → pr
  1. 1r ∧ ¬p
  2. 2¬r
  3. 3p
  4. 4¬p

Answer key

  1. 1. N = 3
  2. 2. N = 8
  3. 3. (q ∨ r) ∧ (q ∨ p)
  4. 4. p ↔ ¬q
  5. 5. ∃x ¬A(x)
  6. 6. p

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