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

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

(¬c → b) ∧ ((a → c) ∧ b)
N =
2.Easy
pq(p → ¬q) ∧ (¬p ∧ ¬q)11?10?01?00?

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

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

Which formula is logically equivalent to c ↔ b? Click it.

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

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

q ∧ (r ∨ p)
  1. 1(q ∧ r) ∨ (q ∧ p)
  2. 2(q ∨ r) ∧ (q ∨ p)
  3. 3q ∨ (r ∧ p)
  4. 4(q ∧ r) ∨ p
5.Hard
¬rr¬qq ∧ ¬r

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

q → rq
  1. 1¬r
  2. 2r
  3. 3¬q
  4. 4q ∧ ¬r
6.Hard
pqrp → (r ∨ q)pr111110101100011010001000

The argument with premises p → (r ∨ q); p and conclusion r is invalid. Click the row of the truth table that is a counterexample.

p → (r ∨ q)p∴ r
  1. 1p = 1, q = 1, r = 1
  2. 2p = 1, q = 1, r = 0
  3. 3p = 1, q = 0, r = 1
  4. 4p = 1, q = 0, r = 0
  5. 5p = 0, q = 1, r = 1
  6. 6p = 0, q = 1, r = 0
  7. 7p = 0, q = 0, r = 1
  8. 8p = 0, q = 0, r = 0

Answer key

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

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