हिंदी

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

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प्रश्न

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

विकल्प

  • Converse

  • Contrapositive

  • Inverse

  • Alternative

MCQ
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उत्तर

Contrapositive

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अध्याय 1.1: Mathematical Logic - MCQ

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).


Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


Evaluate: ∫ x . log x dx


Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Write the following compound statement symbolically. 

Hima Das wins gold medal if and only if she runs fast.


Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p


Construct the truth table of the following statement pattern.

(q → p) ∨ (∼ p ↔ q)


Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ q)]


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


Write the truth value of the following statement.

The Himalayas are the highest mountains but they are part of India in the North East.


Write the truth value of the negation of the following statement.

`sqrt5` is an irrational number.


Write the truth value of the negation of the following statement.

London is in England.


Write the following statement in symbolic form.

Stock prices are high if and only if stocks are rising.


Find the truth value of the following statement.

Neither 27 is a prime number nor divisible by 4.


Find the truth value of the following statement.

3 is a prime number and an odd number.


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ∨ (r ∧ s) 


If p and q are true and r and s are false, find the truth value of the following compound statement.

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]


If p and q are true and r and s are false, find the truth value of the following compound statement.

~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

~ (p ∨ q)


Negation of “some men are animal” is ______.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

The drug is effective though it has side effects.


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r :
Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∨ r


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ p ∨ q


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → q


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If price increases, then demand falls.


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If demand falls, then price does not increase.


Write the negation of the following.

If ∆ABC is not equilateral, then it is not equiangular.


Rewrite the following statement without using the connective ‘If ... then’.

If a quadrilateral is rhombus then it is not a square.


Consider the following statements.

  1. If D is dog, then D is very good.
  2. If D is very good, then D is dog.
  3. If D is not very good, then D is not a dog.
  4. If D is not a dog, then D is not very good. 

Identify the pairs of statements having the same meaning. Justify.


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


Choose the correct alternative:

A biconditional statement is the conjunction of two ______ statements


State whether the following statement is True or False:

The converse of inverse of ~ p → q is q → ~ p


Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______ 


The negation of (p ∨ ∼q) ∧ q is ______


The inverse of the statement "If its quality is good. then it is expensive.", is ______ 


The statement, 'If I go to school, then I will get knowledge' is equivalent to ______ 


The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______


Let p, q and r be any three logical statements. Which of the following is true?


The statement ∼(p ↔ ∼q) is ______.


Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.


If p, q are true statements and r, s are false statements, then write the truth value of the compound statement

(p `→` ∼ r) `→` (q ∧ s)


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