हिंदी

Choose the correct alternative: If p → q is an implication , then the implication ~q → ~p is called its - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

If p → q is an implication, then the implication ~q → ~p is called its

विकल्प

  • Converse

  • Contrapositive

  • Inverse

  • Alternative

MCQ

उत्तर

Contrapositive

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.1: Mathematical Logic - Q.1

संबंधित प्रश्न

Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`


Write the negation of the following statement : 
If the lines are parallel then their slopes are equal.


Using the truth table prove the following logical equivalence.

∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p


Using the truth table prove the following logical equivalence.

p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]


Using the truth table prove the following logical equivalence.

p → (q ∧ r) ≡ (p → q) ∧ (p → r)


Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

[(p → q) ∧ ∼ q] → ∼ p


Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

(p ↔ q) ∧ (p → ∼ q)


Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

(p ∧ ∼ q) ↔ (p → q)


Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .


Determine whether the following statement pattern is a tautology, contradiction or contingency:

[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


If p is any statement then (p ∨ ∼p) is a ______.


Show that the following statement pattern is contingency.

p ∧ [(p → ~ q) → q]


Write the dual statement of the following compound statement.

Radha and Sushmita cannot read Urdu.


Write the negation of the following statement.

All the stars are shining if it is night.


What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.


Determine whether the following statement pattern is a tautology, contradiction, or contingency.

[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ q)]


Using the truth table, prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


Using the truth table, prove the following logical equivalence.

[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


Write the converse, inverse, contrapositive of the following statement.

If I do not work hard, then I do not prosper.


State the dual of the following statement by applying the principle of duality.

(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)


State the dual of the following statement by applying the principle of duality.

2 is even number or 9 is a perfect square.


Write the dual of the following.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (q ∨ r)


Express the truth of the following statement by the Venn diagram.

Some members of the present Indian cricket are not committed.


Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”


If p → (∼p v q) is false, then the truth values of p and q are respectively


The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______. 


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


Determine whether the following statement pattern is a tautology, contradiction, or contingency:

[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)


The statement pattern (∼ p ∧ q) is logically equivalent to ______.


If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______


The converse of contrapositive of ∼p → q is ______.


Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

(p ∧ q) → (q ∨ p)


Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×