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 (q ∧ ¬r) ∨ ((r → p) ∧ p) is written out. In how many rows N is p = 1 and r = 0?

(q ∧ ¬r) ∨ ((r → p) ∧ p)
N =
2.Easy
abc(¬a → c) ↔ ¬b111?110?101?100?011?010?001?000?

Complete the truth table (1 = true, 0 = false). In how many rows N is (¬a → c) ↔ ¬b true?

(¬a → c) ↔ ¬b
N =
3.Medium
pqrq ∧ (r ∨ ¬p)¬(q ∧ (r ∨ ¬p))(q ∨ r) ∧ ¬(q ∧ (r ∨ ¬p))111?110?101?100?011?010?001?000?

In how many of the 8 rows of its truth table is (q ∨ r) ∧ ¬(q ∧ (r ∨ ¬p)) true? Call this number N.

(q ∨ r) ∧ ¬(q ∧ (r ∨ ¬p))
N =
4.Medium
¬¬q → ¬pp → ¬q¬p → ¬¬q¬q ∧ ¬p

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

¬q → p
  1. 1¬¬q → ¬p
  2. 2p → ¬q
  3. 3¬p → ¬¬q
  4. 4¬q ∧ ¬p
5.Hard
∀x (P(x) ∧ ¬Q(x))∀x (¬P(x) → ¬Q(x))∃x (P(x) ∧ ¬Q(x))∀x (P(x) → ¬Q(x))

Which statement is equivalent to ¬∃x (P(x) → Q(x)), with the negation moved all the way inside? Click it.

¬∃x (P(x) → Q(x))
  1. 1∀x (P(x) ∧ ¬Q(x))
  2. 2∀x (¬P(x) → ¬Q(x))
  3. 3∃x (P(x) ∧ ¬Q(x))
  4. 4∀x (P(x) → ¬Q(x))
6.Hard
c ∧ ¬bcb¬c

The premises (a ∧ c) → b; a; ¬b are given. Which conclusion follows from them? Click it.

(a ∧ c) → ba¬b
  1. 1c ∧ ¬b
  2. 2c
  3. 3b
  4. 4¬c

Answer key

  1. 1. N = 2
  2. 2. N = 4
  3. 3. N = 3
  4. 4. ¬p → ¬¬q
  5. 5. ∀x (P(x) ∧ ¬Q(x))
  6. 6. ¬c

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