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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy

The complete truth table of (c ∨ (b ∨ a)) ↔ (b → (¬a → c)) is written out. In how many rows N is b = 1 and c = 0?

(c ∨ (b ∨ a)) ↔ (b → (¬a → c))
N =
2.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 =
3.Medium
¬q → ¬rr ∧ ¬qq → r¬r → ¬q

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

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

You want to prove (p ∧ q) → r by contradiction. Which statement do you assume at the start? Click it.

(p ∧ q) → r
  1. 1(p ∧ q) ∧ ¬r
  2. 2¬(p ∧ q) → ¬r
  3. 3¬(p ∧ q) ∧ ¬r
  4. 4¬(p ∧ q) ∧ r
5.Hard
∀x (¬F(x) → ¬G(x))∃x (F(x) ∧ ¬G(x))∀x (F(x) → ¬G(x))∀x (F(x) ∧ ¬G(x))

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

¬∃x (F(x) → G(x))
  1. 1∀x (¬F(x) → ¬G(x))
  2. 2∃x (F(x) ∧ ¬G(x))
  3. 3∀x (F(x) → ¬G(x))
  4. 4∀x (F(x) ∧ ¬G(x))
6.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)

Answer key

  1. 1. N = 2
  2. 2. N = 3
  3. 3. ¬q → ¬r
  4. 4. (p ∧ q) ∧ ¬r
  5. 5. ∀x (F(x) ∧ ¬G(x))
  6. 6. ∃x ¬A(x)

Full step-by-step solutions: practise this topic on examproblems.com.