Previous Year Questions
Sample Questions (From Textbook)
Q1:- Use truth tables to verify these equivalences.
(a) p ∧ T ≡ p
(b) p ∨ F ≡ p
(c) p ∧ F ≡ F
(d) p ∨ T ≡ T
(e) p ∨ p ≡ p
(f) p ∧ p ≡ p
Q2:- Show that ¬(¬p) and p are logically equivalent.
Q3:- Use truth tables to verify the commutative laws
(a) p ∨ q ≡ q ∨ p.
(b) p ∧ q ≡ q ∧ p.
Q4:- Use truth tables to verify the associative laws
(a) (p ∨ q) ∨ r ≡ p ∨ (q ∨ r).
Q5:- Use De Morgan's laws to find the negation of each of the following statements.
(a) Kwame will take a job in industry or go to graduate school.
(b) Yoshiko knows Java and calculus.
(c) James is young and strong.
(d) Rita will move to Oregon or Washington.
Q6:- Show that each of these conditional statements is a tautology by using truth tables.
(a) (p ∧ q) → p
(b) p → (p ∧ q)
(c) ¬p → (p → q)
(d) (p ∧ q) → (p → q)
(e) ¬(p → q) → p
(f) ¬(p → q) → ¬q
Q7:- Show that each of these conditional statements is a tautology by using truth tables.
(a) [¬p ∧ (p ∧ q)] → q
(b) [(p → q) ∧ (q → r)] → (p → r)
(c) [p ∧ (p → q)] → q
(d) [(p ∧ q) ∧ (p → r) ∧ (q → r)] → r
Q8:- Show that each of these conditional statements is a tautology without using truth tables.
(a) (p ∧ q) → p
(b) p → (p ∧ q)
(c) ¬p → (p → q)
(d) (p ∧ q) → (p → q)
(e) ¬(p → q) → p
(f) ¬(p → q) → ¬q
Q9:- Show that each of these conditional statements is a tautology without using truth tables.
(a) [¬p ∧ (p ∧ q)] → q
(b) [(p → q) ∧ (q → r)] → (p → r)
(c) [p ∧ (p → q)] → q
(d) [(p ∧ q) ∧ (p → r) ∧ (q → r)] → r
Q10:- Show that p | q is logically equivalent to ¬(p ∧ q).
