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
pqr¬(p ∨ ¬q) → ¬r111?110?101?100?011?010?001?000?

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

¬(p ∨ ¬q) → ¬r
N =
2.Easy
pq¬(p ∧ (p ↔ ¬q))11100100

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

¬(p ∧ (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 ∨ ¬qp ∨ ¬q¬p ∧ ¬q¬p ∧ q

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

¬(p ∨ q)
  1. 1¬p ∨ ¬q
  2. 2p ∨ ¬q
  3. 3¬p ∧ ¬q
  4. 4¬p ∧ q
4.Medium
(b → a) ∨ (a → b)b ∧ a(b → a) ∧ (a → b)(b → a) ∧ (¬a → ¬b)

Which formula is logically equivalent to b ↔ a? Click it.

b ↔ a
  1. 1(b → a) ∨ (a → b)
  2. 2b ∧ a
  3. 3(b → a) ∧ (a → b)
  4. 4(b → a) ∧ (¬a → ¬b)
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

How many of the 16 rows of the truth table make ((c ∨ a) ∨ (d ∧ b)) ∧ (c ↔ (d ∨ b)) true? Call this number N.

((c ∨ a) ∨ (d ∧ b)) ∧ (c ↔ (d ∨ b))
N =

Answer key

  1. 1. N = 7
  2. 2. p = 1, q = 0
  3. 3. ¬p ∧ ¬q
  4. 4. (b → a) ∧ (a → b)
  5. 5. ∀x ¬A(x)
  6. 6. N = 7

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