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
abcc ∧ ¬(a ∨ b)111?110?101?100?011?010?001?000?

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

c ∧ ¬(a ∨ b)
N =
2.Easy

The complete truth table of (q ↔ ¬r) ∧ ((¬q ∧ ¬r) ∧ p) is written out. In how many rows N is p = 1 and q = 0?

(q ↔ ¬r) ∧ ((¬q ∧ ¬r) ∧ p)
N =
3.Medium
pqrp ↔ ¬rp → (p ↔ ¬r)(q ∧ (q → r)) ∧ (p → (p ↔ ¬r))111?110?101?100?011?010?001?000?

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

(q ∧ (q → r)) ∧ (p → (p ↔ ¬r))
N =
4.Medium
pqr¬r¬(¬p ∧ ¬q) ∧ ¬r¬(p → r) ∧ (¬(¬p ∧ ¬q) ∧ ¬r)111?110?101?100?011?010?001?000?

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

¬(p → r) ∧ (¬(¬p ∧ ¬q) ∧ ¬r)
N =
5.Hard
pqrr → (p ∨ q)rp111110101100011010001000

The argument with premises r → (p ∨ q); r and conclusion p is invalid. Click the row of the truth table that is a counterexample.

r → (p ∨ q)r∴ p
  1. 1p = 1, q = 1, r = 1
  2. 2p = 1, q = 1, r = 0
  3. 3p = 1, q = 0, r = 1
  4. 4p = 1, q = 0, r = 0
  5. 5p = 0, q = 1, r = 1
  6. 6p = 0, q = 1, r = 0
  7. 7p = 0, q = 0, r = 1
  8. 8p = 0, q = 0, r = 0
6.Hard

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

(q ∧ ¬(s ∧ q)) ∨ (¬p → r)
N =

Answer key

  1. 1. N = 1
  2. 2. N = 2
  3. 3. N = 1
  4. 4. N = 2
  5. 5. p = 0, q = 1, r = 1
  6. 6. N = 13

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