Switching Circuits

1. What type of circuit is formed when switches S1 and S2 are connected in series?

A) p ∧ q
B) p ∨ q
C) p → q
D) p ↔ q

Correct Answer: A) p ∧ q

2. What type of circuit is formed when switches S1 and S2 are connected in parallel?

A) p ∧ q
B) p ∨ q
C) p → q
D) p ↔ q

Correct Answer: B) p ∨ q

3. In the context of switching circuits, which of the following represents a lamp glowing?

A) Switch is open
B) Switch is closed
C) Switch is off
D) Switch is disconnected

Correct Answer: B) Switch is closed

4. The symbolic form of the circuit with switches S1, S2, and S3, where the lamp L is on if S1 is closed or both S2 and S3 are closed, is:

A) p ∨ (q ∧ r)
B) p ∧ (q ∨ r)
C) (p ∨ q) ∧ r
D) (p ∧ q) ∨ r

Correct Answer: A) p ∨ (q ∧ r)

5. What is the input-output table for the statement pattern p ∧ q?

A) Only true when both p and q are true
B) True if either p or q is true
C) True if p is true and q is false
D) True if p is false and q is true

Correct Answer: A) Only true when both p and q are true

6. Which of the following statement patterns is a contradiction?

A) p ∨ ~p
B) p ∧ ~p
C) p → q
D) p ↔ q

Correct Answer: B) p ∧ ~p

7. The truth table for which of the following statements is a tautology?

A) (p ∧ q) → (q ∨ p)
B) (p ∨ q) ∧ ~p
C) p → (q ∧ r)
D) p ↔ ~q

Correct Answer: A) (p ∧ q) → (q ∨ p)

8. Which of the following is true for the statement pattern (p → q) ↔ (~p ∨ q)?

A) It is a tautology
B) It is a contradiction
C) It is a contingency
D) It is a variable

Correct Answer: A) It is a tautology

9. The truth table for which statement pattern shows that it is a contradiction?

A) [p → (~q ∨ r)] ↔ ~[p → (q → r)]
B) p → (q ∧ r)
C) (p ∨ q) ∧ r
D) (p → q) ∧ (q → r)

Correct Answer: A) [p → (~q ∨ r)] ↔ ~[p → (q → r)]

10. What is the input-output table for p ∨ q?

A) True if either p or q is true
B) Only true when both p and q are true
C) True if both p and q are false
D) True if p is false and q is true

Correct Answer: A) True if either p or q is true

11. In symbolic logic, if p is "The switch S1 is closed" and q is "The switch S2 is closed," what is the symbolic form for both switches being open?

A) ~p ∧ ~q
B) p ∧ q
C) ~p ∨ ~q
D) p ∨ q

Correct Answer: A) ~p ∧ ~q

12. Which statement represents the negation of "If it is raining, then the game is cancelled"?

A) It is raining and the game is not cancelled
B) If it is not raining, then the game is not cancelled
C) It is not raining or the game is cancelled
D) The game is cancelled and it is not raining

Correct Answer: A) It is raining and the game is not cancelled

13. Which logical equivalence is demonstrated by p → (q ∧ r) ≡ (p ∧ q) → (p → r)?

A) Tautology
B) Contradiction
C) Contingency
D) Variable

Correct Answer: A) Tautology

14. What is the truth table result for the statement pattern (p ∨ q) → p?

A) True in all cases
B) False in all cases
C) True in some cases
D) False in some cases

Correct Answer: C) True in some cases

15. Which statement pattern is considered a contingency?

A) (p ↔ q) ∧ (p → ~q)
B) (p ∧ q) → (q ∨ p)
C) (p → q) ↔ (~p ∨ q)
D) p ∨ ~p

Correct Answer: A) (p ↔ q) ∧ (p → ~q)

16. For which logical equivalence does the truth table show that it is a contradiction?

A) [p → (~q ∨ r)] ↔ ~[p → (q → r)]
B) p → (q ∧ r)
C) (p ∨ q) ∧ r
D) (p → q) ∧ (q → r)