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
pq(q ↔ p) ∧ p11?10?01?00?

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

(q ↔ p) ∧ p
N =
2.Easy
pq(q ↔ p) → q11100100

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

(q ↔ p) → q
  1. 1p = 1, q = 1
  2. 2p = 1, q = 0
  3. 3p = 0, q = 1
  4. 4p = 0, q = 0
3.Medium
¬p ∧ r¬p ∧ ¬rp ∧ ¬r¬p → ¬r

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

p → r
  1. 1¬p ∧ r
  2. 2¬p ∧ ¬r
  3. 3p ∧ ¬r
  4. 4¬p → ¬r
4.Medium
p ∧ ¬q¬q → ¬p¬p → ¬qq → p

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

p → q
  1. 1p ∧ ¬q
  2. 2¬q → ¬p
  3. 3¬p → ¬q
  4. 4q → p
5.Hard
p ∧ rrp¬r

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

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

Answer key

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

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