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
pq¬(q → (q ↔ p))11?10?01?00?

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

¬(q → (q ↔ p))
N =
2.Easy
aba ↔ b11?10?01?00?

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

a ↔ b
N =
3.Medium
c ∧ ¬(a ∧ b)¬c → ¬(a ∧ b)¬(a ∧ b) → ¬c(a ∧ b) → c

You want to prove c → (a ∧ b) by contrapositive. Which implication do you prove instead? Click it.

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

You want to prove (b ∨ a) → c by contrapositive. Which implication do you prove instead? Click it.

(b ∨ a) → c
  1. 1¬(b ∨ a) → ¬c
  2. 2¬c → ¬(b ∨ a)
  3. 3c → (b ∨ a)
  4. 4(b ∨ a) ∧ ¬c
5.Hard
r¬rq ∧ rq

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

q ∨ r¬q
  1. 1r
  2. 2¬r
  3. 3q ∧ r
  4. 4q
6.Hard

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

((r ↔ p) ↔ (s ∧ ¬q)) ∨ ¬((p ∧ s) → (r ∨ ¬q))
N =

Answer key

  1. 1. N = 1
  2. 2. N = 2
  3. 3. ¬(a ∧ b) → ¬c
  4. 4. ¬c → ¬(b ∨ a)
  5. 5. r
  6. 6. N = 8

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