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

The complete truth table of (¬r ∨ (¬q ∧ p)) ∧ (p ↔ r) is written out. In how many rows N is q = 1 and r = 0?

(¬r ∨ (¬q ∧ p)) ∧ (p ↔ r)
N =
2.Easy
ab(a ↔ ¬b) ↔ (¬a ∧ b)11100100

Exactly one row of the truth table makes (a ↔ ¬b) ↔ (¬a ∧ b) false. Click that row.

(a ↔ ¬b) ↔ (¬a ∧ b)
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
3.Medium
q ∨ ¬r¬q ∨ ¬r¬q ∧ ¬r¬q ∧ r

Which formula is logically equivalent to ¬(q ∨ r)? Click it.

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

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

q → (r ∨ p)
  1. 1¬q → ¬(r ∨ p)
  2. 2¬(r ∨ p) → ¬q
  3. 3q ∧ ¬(r ∨ p)
  4. 4(r ∨ p) → q
5.Hard
∃x ¬A(x)∃x A(x)∀x ¬A(x)∀x A(x)

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

¬∀x A(x)
  1. 1∃x ¬A(x)
  2. 2∃x A(x)
  3. 3∀x ¬A(x)
  4. 4∀x A(x)
6.Hard
¬qp¬pq ∧ ¬p

The premises q → p; q are given. Which conclusion follows from them? Click it.

q → pq
  1. 1¬q
  2. 2p
  3. 3¬p
  4. 4q ∧ ¬p

Answer key

  1. 1. N = 2
  2. 2. a = 1, b = 0
  3. 3. ¬q ∧ ¬r
  4. 4. ¬(r ∨ p) → ¬q
  5. 5. ∃x ¬A(x)
  6. 6. p

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