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
abb → a11100100

Exactly one row of the truth table makes b → a false. Click that row.

b → a
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
2.Easy
pqq ∧ (¬q → p)11?10?01?00?

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

q ∧ (¬q → p)
N =
3.Medium
(p → q) ∨ (r → q)(p ∧ r) → q(p → q) ∧ (r → q)p ∨ (r → q)

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

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

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

r → q
  1. 1¬r ∧ q
  2. 2r ∨ ¬q
  3. 3¬r → ¬q
  4. 4¬r ∨ q
5.Hard
r¬rp¬r ∧ p

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

r → qq → p¬p
  1. 1r
  2. 2¬r
  3. 3p
  4. 4¬r ∧ p
6.Hard
aca → cca11100100

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

a → cc∴ a
  1. 1a = 1, c = 1
  2. 2a = 1, c = 0
  3. 3a = 0, c = 1
  4. 4a = 0, c = 0

Answer key

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

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