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
pq¬p → ¬q11100100

Exactly one row of the truth table makes ¬p → ¬q false. Click that row.

¬p → ¬q
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 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
c ∧ ¬b¬c → ¬b¬c ∧ bc → ¬b

Which formula is logically equivalent to ¬(c → b)? Click it.

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

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

(p ∨ q) → r
  1. 1(p → r) ∨ (q → r)
  2. 2(p → r) ∧ (q → r)
  3. 3(p ∧ q) → r
  4. 4p ∨ (q → r)
5.Hard

How many of the 16 rows of the truth table make (b ↔ (¬b → a)) ↔ (d ↔ (d ∧ c)) true? Call this number N.

(b ↔ (¬b → a)) ↔ (d ↔ (d ∧ c))
N =
6.Hard
qp¬pq ∧ r

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

q ∨ rq → pr → p
  1. 1q
  2. 2p
  3. 3¬p
  4. 4q ∧ r

Answer key

  1. 1. p = 0, q = 1
  2. 2. N = 1
  3. 3. c ∧ ¬b
  4. 4. (p → r) ∧ (q → r)
  5. 5. N = 10
  6. 6. p

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