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Name: ____________________ Date: ____________
1.Easy
Exactly one row of the truth table makes (q ∨ ¬p) → ((¬p ∧ q) → r) false. Click that row.
(q ∨ ¬p) → ((¬p ∧ q) → r)
1p = 1, q = 1, r = 1
2p = 1, q = 1, r = 0
3p = 1, q = 0, r = 1
4p = 1, q = 0, r = 0
5p = 0, q = 1, r = 1
6p = 0, q = 1, r = 0
7p = 0, q = 0, r = 1
8p = 0, q = 0, r = 0
2.Easy
Complete the truth table (1 = true, 0 = false). In how many rows N is q → (r → ¬p) true?
q → (r → ¬p)
N =
3.Medium
In how many of the 8 rows of its truth table is (¬r ↔ (q → p)) ∧ (¬p ∧ (¬q ∨ ¬r)) true? Call this number N.
(¬r ↔ (q → p)) ∧ (¬p ∧ (¬q ∨ ¬r))
N =
4.Medium
You want to prove (b ∨ c) → a by contrapositive. Which implication do you prove instead? Click it.
(b ∨ c) → a
1(b ∨ c) ∧ ¬a
2¬a → ¬(b ∨ c)
3¬(b ∨ c) → ¬a
4a → (b ∨ c)
5.Hard
How many of the 16 rows of the truth table make (¬q → (r → s)) → ((¬r ↔ ¬q) ∧ ¬p) true? Call this number N.
(¬q → (r → s)) → ((¬r ↔ ¬q) ∧ ¬p)
N =
6.Hard
The premises p ∨ r; ¬p are given. Which conclusion follows from them? Click it.
p ∨ r¬p
1p ∧ r
2p
3¬r
4r
Answer key
1. p = 0, q = 1, r = 0
2. N = 7
3. N = 1
4. ¬a → ¬(b ∨ c)
5. N = 6
6. r
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