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 ¬(¬a ∧ c) ∨ (b ↔ ¬a) have?

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

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

(q → p) ↔ (q → ¬p)
N =
3.Medium
pqr¬(r → p)¬(r → p) ∧ r(¬q ∧ p) ∨ (¬(r → p) ∧ r)111?110?101?100?011?010?001?000?

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

(¬q ∧ p) ∨ (¬(r → p) ∧ r)
N =
4.Medium
(a ∨ b) ∧ (a ∨ c)a ∧ (b ∨ c)(a ∧ b) ∨ (a ∧ c)(a ∨ b) ∧ c

Which formula is logically equivalent to a ∨ (b ∧ c)? Click it.

a ∨ (b ∧ c)
  1. 1(a ∨ b) ∧ (a ∨ c)
  2. 2a ∧ (b ∨ c)
  3. 3(a ∧ b) ∨ (a ∧ c)
  4. 4(a ∨ b) ∧ c
5.Hard

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

(r ↔ q) ∧ ¬(s → p)
N =
6.Hard
q¬q ∧ p¬qp

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

q → rr → p¬p
  1. 1q
  2. 2¬q ∧ p
  3. 3¬q
  4. 4p

Answer key

  1. 1. N = 8
  2. 2. N = 2
  3. 3. N = 4
  4. 4. (a ∨ b) ∧ (a ∨ c)
  5. 5. N = 2
  6. 6. ¬q

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