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 (a → b) → (c → ¬a) is written out. In how many rows N is a = 1 and b = 0?

(a → b) → (c → ¬a)
N =
2.Easy
pq(¬q ∨ ¬p) → (q ↔ ¬p)11?10?01?00?

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

(¬q ∨ ¬p) → (q ↔ ¬p)
N =
3.Medium
¬c → ¬b¬b → ¬cc → b¬c ∧ ¬b

Which formula is logically equivalent to b → c? Click it.

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

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

(¬p ∨ r) ∨ (q ∨ r)
N =
5.Hard
r¬q¬q ∧ rq

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

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

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

p ∨ q¬p ∨ r
  1. 1q ∨ r
  2. 2p ∨ r
  3. 3q ∧ r
  4. 4¬q

Answer key

  1. 1. N = 2
  2. 2. N = 3
  3. 3. ¬c → ¬b
  4. 4. N = 7
  5. 5. ¬q
  6. 6. q ∨ r

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