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
ab(a ↔ b) → a11100100

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

(a ↔ b) → a
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
2.Easy

How many rows N does the complete truth table of ((r ∧ p) ∧ ¬q) ↔ ((r ∧ p) ∨ q) have?

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

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

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

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

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

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

q → rq
  1. 1r
  2. 2q ∧ ¬r
  3. 3¬r
  4. 4¬q
6.Hard

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

¬((s ∧ (r → ¬p)) ↔ ((¬s → p) → q))
N =

Answer key

  1. 1. a = 0, b = 0
  2. 2. N = 8
  3. 3. ¬¬p → ¬¬q
  4. 4. ¬q → ¬p
  5. 5. r
  6. 6. N = 10

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