Advertisements
Advertisements
प्रश्न
Without using truth table, show that
(p ∨ q) → r ≡ (p → r) ∧ (q → r)
Advertisements
उत्तर
L.H.S.
≡ (p ∨ q) → r
≡ ~ (p ∨ q) ∨ r ....[p → q → ~ p ∨ q]
≡ (~ p ∧ ~ q) ∨ r ....[De Morgan’s law]
≡ (~ p ∨ r) ∧ (~ q ∨ r) .....[Distributive law]
≡ (p → r) ∧ (q → r) .....[p → q → ~ p ∨ q]
= R.H.S.
APPEARS IN
संबंधित प्रश्न
Without using truth tabic show that ~(p v q)v(~p ∧ q) = ~p
If A = {2, 3, 4, 5, 6}, then which of the following is not true?
(A) ∃ x ∈ A such that x + 3 = 8
(B) ∃ x ∈ A such that x + 2 < 5
(C) ∃ x ∈ A such that x + 2 < 9
(D) ∀ x ∈ A such that x + 6 ≥ 9
Using the rules of negation, write the negatlon of the following:
(a) p ∧ (q → r)
(b) ~P ∨ ~q
Write the Truth Value of the Negation of the Following Statement :
The Sun sets in the East.
Rewrite the following statement without using if ...... then.
If a man is a judge then he is honest.
Rewrite the following statement without using if ...... then.
It f(2) = 0 then f(x) is divisible by (x – 2).
Without using truth table prove that:
∼ [(p ∨ ∼ q) → (p ∧ ∼ q)] ≡ (p ∨ ∼ q) ∧ (∼ p ∨ q)
Using rules in logic, prove the following:
∼p ∧ q ≡ (p ∨ q) ∧ ∼p
Using rules in logic, prove the following:
∼ (p ∨ q) ∨ (∼p ∧ q) ≡ ∼p
Using the rules in logic, write the negation of the following:
(p ∨ q) ∧ (q ∨ ∼r)
Using the rules in logic, write the negation of the following:
(∼p ∧ q) ∨ (p ∧ ∼q)
Without using truth table, show that
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Using the algebra of statement, prove that
[p ∧ (q ∨ r)] ∨ [~ r ∧ ~ q ∧ p] ≡ p
(p → q) ∨ p is logically equivalent to ______
The logically equivalent statement of (p ∨ q) ∧ (p ∨ r) is ______
(p ∧ ∼q) ∧ (∼p ∧ q) is a ______.
Without using truth table prove that (p ∧ q) ∨ (∼ p ∧ q) v (p∧ ∼ q) ≡ p ∨ q
If p ∨ q is true, then the truth value of ∼ p ∧ ∼ q is ______.
Negation of the Boolean expression `p Leftrightarrow (q \implies p)` is ______.
Without using truth table, prove that : [(p ∨ q) ∧ ∼p] →q is a tautology.
Without using truth table prove that
[(p ∧ q ∧ ∼ p) ∨ (∼ p ∧ q ∧ r) ∨ (p ∧ q ∧ r) ∨ (p ∧ ∼ q ∧ r) ≡ (p ∨ q) ∧ r
Show that the simplified form of (p ∧ q ∧ ∼ r) ∨ (r ∧ p ∧ q) ∨ (∼ p ∨ q) is q ∨ ∼ p.
