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
ab(a ∨ b) ∨ (b ∧ a)11100100

Exactly one row of the truth table makes (a ∨ b) ∨ (b ∧ a) false. Click that row.

(a ∨ b) ∨ (b ∧ a)
  1. 1a = 1, b = 1
  2. 2a = 1, b = 0
  3. 3a = 0, b = 1
  4. 4a = 0, b = 0
2.Easy

The complete truth table of ¬(((¬a ∧ b) ∧ c) ∨ (c ∧ a)) is written out. In how many rows N is b = 1 and c = 0?

¬(((¬a ∧ b) ∧ c) ∨ (c ∧ a))
N =
3.Medium
q → rr ∨ ¬q¬r ∨ q¬r ∧ q

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

r → q
  1. 1q → r
  2. 2r ∨ ¬q
  3. 3¬r ∨ q
  4. 4¬r ∧ q
4.Medium
¬q → ¬rq → ¬r¬q ∨ ¬rq ∧ ¬r

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

¬(q → r)
  1. 1¬q → ¬r
  2. 2q → ¬r
  3. 3¬q ∨ ¬r
  4. 4q ∧ ¬r
5.Hard
cb ∧ ¬c¬bb

The premises (a ∧ b) → c; a; ¬c are given. Which conclusion follows from them? Click it.

(a ∧ b) → ca¬c
  1. 1c
  2. 2b ∧ ¬c
  3. 3¬b
  4. 4b
6.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)

Answer key

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

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