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
pqp ∨ 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
abb ∧ (b ∨ a)11?10?01?00?

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

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

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

((r ∨ ¬p) → q) ∧ (p ∨ r)
N =
4.Medium
¬q → ¬¬p¬¬p → ¬q¬p ∧ ¬qq → ¬p

You want to prove ¬p → q by contrapositive. Which implication do you prove instead? Click it.

¬p → q
  1. 1¬q → ¬¬p
  2. 2¬¬p → ¬q
  3. 3¬p ∧ ¬q
  4. 4q → ¬p
5.Hard
∀x (F(x) ∧ ¬G(x))∃x (F(x) ∧ ¬G(x))∀x (F(x) → ¬G(x))∃x (F(x) → ¬G(x))

Which statement is equivalent to ¬∀x (F(x) → G(x)), with the negation moved all the way inside? Click it.

¬∀x (F(x) → G(x))
  1. 1∀x (F(x) ∧ ¬G(x))
  2. 2∃x (F(x) ∧ ¬G(x))
  3. 3∀x (F(x) → ¬G(x))
  4. 4∃x (F(x) → ¬G(x))
6.Hard
qrq → rrq11100100

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

q → rr∴ q
  1. 1q = 1, r = 1
  2. 2q = 1, r = 0
  3. 3q = 0, r = 1
  4. 4q = 0, r = 0

Answer key

  1. 1. p = 0, q = 0
  2. 2. N = 2
  3. 3. N = 4
  4. 4. ¬q → ¬¬p
  5. 5. ∃x (F(x) ∧ ¬G(x))
  6. 6. q = 0, r = 1

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