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Name: ____________________ Date: ____________
1.Easy
Exactly one row of the truth table makes (r → ¬(¬p ∧ q)) ↔ (r → p) false. Click that row.
(r → ¬(¬p ∧ q)) ↔ (r → p)
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
The complete truth table of ¬(¬c ↔ (a ↔ b)) → (a ∧ ¬b) is written out. In how many rows N is a = 1 and b = 0?
¬(¬c ↔ (a ↔ b)) → (a ∧ ¬b)
N =
3.Medium
Which formula is logically equivalent to b ↔ c? Click it.
b ↔ c
1(b → c) ∧ (c → b)
2(b → c) ∨ (c → b)
3b ∧ c
4(b → c) ∧ (¬c → ¬b)
4.Medium
In how many of the 8 rows of its truth table is (q ∨ p) ∧ (r → (¬p ∨ q)) true? Call this number N.
(q ∨ p) ∧ (r → (¬p ∨ q))
N =
5.Hard
How many of the 16 rows of the truth table make ((¬b → ¬d) → a) → ((¬b ↔ c) → c) true? Call this number N.
((¬b → ¬d) → a) → ((¬b ↔ c) → c)
N =
6.Hard
Which statement is equivalent to ¬∀x (P(x) → Q(x)), with the negation moved all the way inside? Click it.
¬∀x (P(x) → Q(x))
1∃x (P(x) ∧ ¬Q(x))
2∀x (P(x) → ¬Q(x))
3∃x (¬P(x) ∧ Q(x))
4∀x (P(x) ∧ ¬Q(x))
Answer key
1. p = 0, q = 0, r = 1
2. N = 2
3. (b → c) ∧ (c → b)
4. N = 5
5. N = 14
6. ∃x (P(x) ∧ ¬Q(x))
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