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
pqr(r ↔ q) ∨ ¬p111?110?101?100?011?010?001?000?

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

(r ↔ q) ∨ ¬p
N =
2.Easy

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

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

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

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

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

((r → p) ∧ (r → ¬q)) ∨ (p ∧ q)
N =
5.Hard
a → bb ∧ ab → a¬b → ¬a

The premises b → c; c → a are given. Which conclusion follows from them? Click it.

b → cc → a
  1. 1a → b
  2. 2b ∧ a
  3. 3b → a
  4. 4¬b → ¬a
6.Hard

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

(¬(p → r) ∧ s) ∧ (¬q ∧ (q → s))
N =

Answer key

  1. 1. N = 6
  2. 2. N = 2
  3. 3. N = 4
  4. 4. N = 6
  5. 5. b → a
  6. 6. N = 1

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