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Name: ____________________ Date: ____________
1.Easy
Exactly one row of the truth table makes (r ↔ (q ↔ p)) → (¬q ∨ r) false. Click that row.
(r ↔ (q ↔ 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
The complete truth table of ¬((r ∧ p) → (q ∨ (q → p))) is written out. In how many rows N is p = 1 and r = 0?
¬((r ∧ p) → (q ∨ (q → p)))
N =
3.Medium
Which formula is logically equivalent to (p ∧ r) → q? Click it.
(p ∧ r) → q
1(p → r) → q
2p ∧ (r → q)
3(p → q) ∧ (r → q)
4p → (r → q)
4.Medium
In how many of the 8 rows of its truth table is (p ∨ (¬r ↔ p)) ∧ (r → q) true? Call this number N.
(p ∨ (¬r ↔ p)) ∧ (r → q)
N =
5.Hard
The premises r → q; q → p are given. Which conclusion follows from them? Click it.
r → qq → p
1r → p
2p → r
3¬r → ¬p
4r ∧ p
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 = 1, r = 0
2. N = 2
3. p → (r → q)
4. N = 4
5. r → p
6. ∀x (P(x) ∧ ¬Q(x))
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