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

How many rows N does the complete truth table of ¬(¬(p ∧ ¬(¬q → r)) ∧ (¬q ∨ p)) have?

¬(¬(p ∧ ¬(¬q → r)) ∧ (¬q ∨ p))
N =
2.Easy
aba ↔ b11?10?01?00?

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

a ↔ b
N =
3.Medium
¬b → ¬¬ab → ¬a¬a ∧ ¬b¬¬a → ¬b

You want to prove ¬a → b by contrapositive. Which implication do you prove instead? Click it.

¬a → b
  1. 1¬b → ¬¬a
  2. 2b → ¬a
  3. 3¬a ∧ ¬b
  4. 4¬¬a → ¬b
4.Medium
pqr¬p¬p ∨ q(r ∨ (q ∧ ¬r)) ∧ (¬p ∨ q)111?110?101?100?011?010?001?000?

In how many of the 8 rows of its truth table is (r ∨ (q ∧ ¬r)) ∧ (¬p ∨ q) true? Call this number N.

(r ∨ (q ∧ ¬r)) ∧ (¬p ∨ q)
N =
5.Hard
∀x (¬P(x) → ¬Q(x))∀x (P(x) ∧ ¬Q(x))∀x (P(x) → ¬Q(x))∃x (P(x) ∧ ¬Q(x))

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

¬∃x (P(x) → Q(x))
  1. 1∀x (¬P(x) → ¬Q(x))
  2. 2∀x (P(x) ∧ ¬Q(x))
  3. 3∀x (P(x) → ¬Q(x))
  4. 4∃x (P(x) ∧ ¬Q(x))
6.Hard

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

(q ∨ (s ∨ p)) → (¬r ∨ ¬(s → ¬p))
N =

Answer key

  1. 1. N = 8
  2. 2. N = 2
  3. 3. ¬b → ¬¬a
  4. 4. N = 5
  5. 5. ∀x (P(x) ∧ ¬Q(x))
  6. 6. N = 11

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