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
ab(a → b) → (¬b ∧ ¬a)11?10?01?00?

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

(a → b) → (¬b ∧ ¬a)
N =
2.Easy
pq¬p ↔ (p → q)11100100

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

¬p ↔ (p → q)
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
3.Medium
pqr¬p(p ∨ q) ↔ ¬p(¬q ∨ r) ∨ ((p ∨ q) ↔ ¬p)111?110?101?100?011?010?001?000?

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

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

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

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

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

(p ∨ ¬s) → ((p ↔ q) → r)
N =
6.Hard
bcb → c¬b¬c11100100

The argument with premises b → c; ¬b and conclusion ¬c is invalid. Click the row of the truth table that is a counterexample.

b → c¬b∴ ¬c
  1. 1b = 1, c = 1
  2. 2b = 1, c = 0
  3. 3b = 0, c = 1
  4. 4b = 0, c = 0

Answer key

  1. 1. N = 2
  2. 2. p = 1, q = 1
  3. 3. N = 7
  4. 4. (c ∧ a) ∨ (c ∧ b)
  5. 5. N = 13
  6. 6. b = 0, c = 1

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