हिंदी

Using the Rules of Negation, Write the Negatlon of the Following: - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Using the rules of negation, write the negatlon of the following: 

(a) p ∧ (q → r)

(b)  ~P ∨ ~q

योग

उत्तर

(a) p ∧ (q → r)

~[p ∧ ~ (q → r)]

≡ ~ p ∨ ~ (q → r )

≡ ~ p ∨ ~ (q ∧ ~ r )

(b)  ~P ∨ ~q

~[~p ∨ ~q]

≡ ~(~p) ∧ ~(~q)

≡ P  ∧ q

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2017-2018 (July) Set 1

APPEARS IN

संबंधित प्रश्न

The negation of p ∧ (q → r) is ______________.


Without using truth tabic show that ~(p v q)v(~p ∧ q) = ~p


Without using the truth table show that P ↔ q ≡ (p ∧ q) ∨ (~ 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.

It 2 is a rational number then `sqrt2` is irrational number.


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


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 ∨ 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)


Without using truth table, show that

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


Without using truth table, show that

p ∧ [(~ p ∨ q) ∨ ~ q] ≡ p


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


For any two statements p and q, the negation of the expression (p ∧ ∼q) ∧ ∼p is ______ 


(p → q) ∨ p is logically equivalent to ______ 


The logically equivalent statement of (p ∨ q) ∧ (p ∨ r) is ______ 


(p ∧ ∼q) ∧ (∼p ∧ q) is a ______.


The negation of the Boolean expression (r ∧ ∼s) ∨ s 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 ______.


∼ ((∼ p) ∧ q) is equal to ______.


Without using truth table, prove that:

[p ∧ (q ∨ r)] ∨ [∼r ∧ ∼q ∧ p] ≡ p


Without using truth table, prove that : [(p ∨ q) ∧ ∼p] →q is a tautology.


The simplified form of [(~ p v q) ∧ r] v [(p ∧ ~ q) ∧ r] is ______.


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×