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
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 =
2.Easy
ab(a → b) ∧ (¬a ∧ b)11100100

Exactly one row of the truth table makes (a → b) ∧ (¬a ∧ b) true. 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
¬r → ¬qr → q¬q → ¬r¬r ∧ ¬q

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

q → r
  1. 1¬r → ¬q
  2. 2r → q
  3. 3¬q → ¬r
  4. 4¬r ∧ ¬q
4.Medium
pqr¬rq ∧ ¬r(r ∨ (q → p)) ↔ (q ∧ ¬r)111?110?101?100?011?010?001?000?

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

(r ∨ (q → p)) ↔ (q ∧ ¬r)
N =
5.Hard
∀x ¬F(x)∀x F(x)∃x F(x)∃x ¬F(x)

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

¬∀x F(x)
  1. 1∀x ¬F(x)
  2. 2∀x F(x)
  3. 3∃x F(x)
  4. 4∃x ¬F(x)
6.Hard

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

(b ∨ ¬(a → ¬b)) ∨ (d ∨ (c ∧ a))
N =

Answer key

  1. 1. N = 4
  2. 2. a = 0, b = 1
  3. 3. ¬r → ¬q
  4. 4. N = 1
  5. 5. ∃x ¬F(x)
  6. 6. N = 13

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