Advertisements
Advertisements
प्रश्न
Without using the truth table show that P ↔ q ≡ (p ∧ q) ∨ (~ p ∧ ~ q)
Advertisements
उत्तर
L.H.S = p ↔ q
≡ (p → q) ∧ (q → p) ........(Biconditional Law)
≡ (∼ p ∨ q) ∧ (∼ q ∨ p) ........(Conditional Law)
≡ [∼ p ∧ (∼ q ∨ p)] ∨ [q ∧ (∼ q ∨ p)] ....(Distributive Law)
≡ [(∼ p ∧ ∼ q)] ∨ (∼ p ∧ p)] ∨ [(q ∧ ∼ q) ∨ (q ∧ p)] .........(Distributive Law)
≡ [(∼ p ∧ ∼ q) ∨ F] ∨ [F ∨ (q ∧ p)] ........(Complement Law)
≡ (∼ p ∧ ∼ q) ∨ (q ∧ p) .......(Identity Law)
≡ (∼ p ∧ ∼ q) ∨ (p ∧ q) ........(Commutative Law)
≡ (p ∧ q) ∨ (∼ p ∧ ∼ q) ........(Commutative Law)
≡ R.H.S.
APPEARS IN
संबंधित प्रश्न
The negation of p ∧ (q → r) is ______________.
Without using truth tabic show that ~(p v q)v(~p ∧ q) = ~p
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 2 is a rational number then `sqrt2` is irrational number.
Without using truth table prove that:
(p ∨ q) ∧ (p ∨ ∼ q) ≡ p
Using rules in logic, prove the following:
p ↔ q ≡ ∼(p ∧ ∼q) ∧ ∼(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 ∨ r)
Using the rules in logic, write the negation of the following:
(p → q) ∧ r
Using the rules in logic, write the negation of the following:
(∼p ∧ q) ∨ (p ∧ ∼q)
Let p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r). Then, this law is known as ______.
Without using truth table, show that
p ∧ [(~ p ∨ q) ∨ ~ q] ≡ p
Without using truth table, show that
~ [(p ∧ q) → ~ q] ≡ p ∧ q
Without using truth table, show that
~r → ~ (p ∧ q) ≡ [~ (q → r)] → ~ p
Using the algebra of statement, prove that
[p ∧ (q ∨ r)] ∨ [~ r ∧ ~ q ∧ p] ≡ p
Using the algebra of statement, prove that
(p ∧ q) ∨ (p ∧ ~ q) ∨ (~ p ∧ ~ q) ≡ (p ∨ ~ q)
Using the algebra of statement, prove that (p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ (~ p ∧ q).
The statement pattern p ∧ ( q v ~ p) is equivalent to ______.
(p → q) ∨ p is logically equivalent to ______
The logically equivalent statement of (p ∨ q) ∧ (p ∨ r) is ______
The statement pattern p ∧ (∼p ∧ q) is ______.
The statement pattern [∼r ∧ (p ∨ q) ∧ (p ∨ q) ∧ (∼p ∧ q)] is equivalent to ______
(p ∧ ∼q) ∧ (∼p ∧ q) is a ______.
The negation of the Boolean expression (r ∧ ∼s) ∨ s is equivalent to: ______
The logical statement [∼(q ∨ ∼r) ∨ (p ∧ r)] ∧ (q ∨ p) is equivalent to: ______
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 ______.
Which of the following is not a statement?
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
The statement p → (q → p) is equivalent to ______.
Show that the simplified form of (p ∧ q ∧ ∼ r) ∨ (r ∧ p ∧ q) ∨ (∼ p ∨ q) is q ∨ ∼ p.
