For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.
Name: ____________________ Date: ____________
1.Easy
Exactly one row of the truth table makes (¬a ↔ b) → (c ↔ (b ∧ c)) false. Click that row.
(¬a ↔ b) → (c ↔ (b ∧ c))
1a = 1, b = 1, c = 1
2a = 1, b = 1, c = 0
3a = 1, b = 0, c = 1
4a = 1, b = 0, c = 0
5a = 0, b = 1, c = 1
6a = 0, b = 1, c = 0
7a = 0, b = 0, c = 1
8a = 0, b = 0, c = 0
2.Easy
Exactly one row of the truth table makes (p → q) ↔ p true. Click that row.
(p → q) ↔ p
1p = 1, q = 1
2p = 1, q = 0
3p = 0, q = 1
4p = 0, q = 0
3.Medium
Which formula is logically equivalent to ¬(r ↔ q)? Click it.
¬(r ↔ q)
1r ↔ ¬q
2¬r ∨ ¬q
3¬r ↔ ¬q
4r ∧ ¬q
4.Medium
Is (b → c) ∧ (b ∧ ¬c) a tautology, a contradiction or a contingency? Click your answer.
(b → c) ∧ (b ∧ ¬c)
1tautology
2contradiction
3contingency
5.Hard
The premises p → r; r → q; ¬q are given. Which conclusion follows from them? Click it.
p → rr → q¬q
1q
2¬p ∧ q
3¬p
4p
6.Hard
Which statement is equivalent to ¬∃x A(x), with the negation moved all the way inside? Click it.
¬∃x A(x)
1∀x A(x)
2∀x ¬A(x)
3∃x ¬A(x)
4∃x A(x)
Answer key
1. a = 1, b = 0, c = 1
2. p = 1, q = 1
3. r ↔ ¬q
4. contradiction
5. ¬p
6. ∀x ¬A(x)
Full step-by-step solutions: practise this topic on examproblems.com.