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 ((¬p ∧ q) ↔ (r ↔ ¬q)) ∧ ¬(p → ¬r) have?

((¬p ∧ q) ↔ (r ↔ ¬q)) ∧ ¬(p → ¬r)
N =
2.Easy
pq¬q ∨ p11?10?01?00?

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

¬q ∨ p
N =
3.Medium
¬a ∧ b¬a ∨ ¬b¬a ∨ b¬a ∧ ¬b

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

¬(a ∧ b)
  1. 1¬a ∧ b
  2. 2¬a ∨ ¬b
  3. 3¬a ∨ b
  4. 4¬a ∧ ¬b
4.Medium
¬q ∨ ¬r¬q ∧ rq ∨ ¬r¬q ∧ ¬r

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

¬(q ∨ r)
  1. 1¬q ∨ ¬r
  2. 2¬q ∧ r
  3. 3q ∨ ¬r
  4. 4¬q ∧ ¬r
5.Hard

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

(¬r → (p ∧ q)) ↔ ((¬r ∧ ¬p) ∨ s)
N =
6.Hard
∃y ∀x ¬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∃y ∀x ¬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 = 8
  2. 2. N = 3
  3. 3. ¬a ∨ ¬b
  4. 4. ¬q ∧ ¬r
  5. 5. N = 6
  6. 6. ∃x ∀y ¬R(x, y)

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