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 ∨ (a ∧ b)11?10?01?00?

Complete the truth table (1 = true, 0 = false). In how many rows N is b ∨ (a ∧ b) true?

b ∨ (a ∧ b)
N =
2.Easy
aba ∨ b11100100

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

a ∨ b
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
3.Medium
(c ∧ a) → b(c → b) ∨ (a → b)(c → b) ∧ (a → b)c ∨ (a → b)

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

(c ∨ a) → b
  1. 1(c ∧ a) → b
  2. 2(c → b) ∨ (a → b)
  3. 3(c → b) ∧ (a → b)
  4. 4c ∨ (a → b)
4.Medium
¬a → ¬(b ∨ c)¬a ∧ ¬(b ∨ c)a ∧ ¬(b ∨ c)¬a ∧ (b ∨ c)

You want to prove a → (b ∨ c) by contradiction. Which statement do you assume at the start? Click it.

a → (b ∨ c)
  1. 1¬a → ¬(b ∨ c)
  2. 2¬a ∧ ¬(b ∨ c)
  3. 3a ∧ ¬(b ∨ c)
  4. 4¬a ∧ (b ∨ c)
5.Hard
∃y ∀x ¬R(x, y)∃x ∀y ¬R(x, y)∀x ∃y ¬R(x, y)∀x ∀y ¬R(x, y)

Which statement is equivalent to ¬∀x ∃y R(x, y), with the negation moved all the way inside? Click it.

¬∀x ∃y R(x, y)
  1. 1∃y ∀x ¬R(x, y)
  2. 2∃x ∀y ¬R(x, y)
  3. 3∀x ∃y ¬R(x, y)
  4. 4∀x ∀y ¬R(x, y)
6.Hard

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

¬((¬d ∧ ¬b) ∨ c) ∧ ((a ∧ d) → c)
N =

Answer key

  1. 1. N = 2
  2. 2. a = 0, b = 0
  3. 3. (c → b) ∧ (a → b)
  4. 4. a ∧ ¬(b ∨ c)
  5. 5. ∃x ∀y ¬R(x, y)
  6. 6. N = 4

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