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 ((r → ¬p) ∨ r) → (q ∨ p) have?

((r → ¬p) ∨ r) → (q ∨ p)
N =
2.Easy
pqrp ∧ (q → r)111?110?101?100?011?010?001?000?

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

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

Which formula is logically equivalent to r → q? Click it.

r → q
  1. 1r ∨ ¬q
  2. 2¬r → ¬q
  3. 3q → r
  4. 4¬r ∨ q
4.Medium
¬q ∧ (r ∧ p)¬q ∧ ¬(r ∧ p)q ∧ ¬(r ∧ p)¬q → ¬(r ∧ p)

You want to prove q → (r ∧ p) by contradiction. Which statement do you assume at the start? Click it.

q → (r ∧ p)
  1. 1¬q ∧ (r ∧ p)
  2. 2¬q ∧ ¬(r ∧ p)
  3. 3q ∧ ¬(r ∧ p)
  4. 4¬q → ¬(r ∧ p)
5.Hard
bcb ∨ cb¬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 ∨ cb∴ ¬c
  1. 1b = 1, c = 1
  2. 2b = 1, c = 0
  3. 3b = 0, c = 1
  4. 4b = 0, c = 0
6.Hard
rqr ∧ q¬q

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

r ∨ q¬r
  1. 1r
  2. 2q
  3. 3r ∧ q
  4. 4¬q

Answer key

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

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