हिंदी

If p → q is an implication, then the implication ∼ q → ∼ p is called its - Mathematics and Statistics

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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

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.

Angle is neither acute nor obtuse.


Construct the truth table of the following statement pattern.

(∼ p → ∼ q) ∧ (∼ q → ∼ p)


Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ q)]


Construct the truth table of the following:

∼ (∼p ∧ ∼q) ∨ q


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Express the following statement in symbolic form.

I like playing but not singing.


Write the negation of the following statement.

It is false that Nagpur is capital of Maharashtra


Write the negation of the following statement.

2 + 3 ≠ 5


Write the following statement in symbolic form.

Even though it is not cloudy, it is still raining.


Write the following statement in symbolic form.

Milk is white if and only if the sky is not blue.


Write the following statement in symbolic form.

If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.


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) ↔ ~(p ∨ q)


Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

Sunday is a holiday and Ram studies on holiday.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement:

p ↔ ~ q


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

The Sun has set and Moon has risen.


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

3 is prime number if 3 is perfect square number.


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

The necessary condition for existence of a tangent to the curve of the function is continuity.


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.


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

If a real number is not rational, then it must be irrational.


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

It is not true that intelligent persons are neither polite nor helpful.


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 → 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


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.

An angle is a right angle if and only if it is of measure 90°.


Write the negation of the following.

Kanchanganga is in India and Everest is in Nepal.


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.


Write the negation of the following statement.

10 > 5 and 3 < 8


Write the negation of the following statement.

∃ x ∈ A, such that x + 5 < 11.


The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.


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


Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra


Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)


Without using truth table show that -

(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)


State whether the following statement is True or False:

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


Negation of “Some men are animal” is ______.


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


Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra


If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.


The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______


The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______


The statement ∼(p ↔ ∼q) is ______.


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


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