मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

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

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प्रश्न

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

पर्याय

  • p ˄ q ˄ ∼ r

  • (p ˄ q) ˅ r

  • p ˅ q ˅ ∼ r

  • (p v q) ˄ (r ˅ s)

MCQ
रिकाम्या जागा भरा
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उत्तर

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

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पाठ 1.1: Mathematical Logic - MCQ

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls


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


Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p


Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


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


Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p


Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)


Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∨ q) → q is F


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Express the following statement in symbolic form.

Milk is white or grass is green.


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

For every x ∈ N, x + 3 < 8.


Write the following statement in symbolic form.

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


Write the following statement in symbolic form.

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


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

~ [(~ p ∨ s) ∧ (~ q ∧ r)]


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]


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 not holiday or Ram studies on holiday.


Fill in the blanks :

Conjunction of two statement p and q is symbolically written as ______.


Negation of “some men are animal” is ______.


State whether the following statement is True or False:

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.


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.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

It is not true that the proof is lengthy but it is interesting.


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)


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

If price increases, then demand falls.


Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.


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

If 10 − 3 = 7 then 10 × 3 ≠ 30.


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

If it rains then the principal declares a holiday.


Write the negation of the following statement.

∃ x ∈ A, such that x + 5 < 11.


Negation of p → (p ˅ ∼ q) is ______


Write the following statements in symbolic form

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


Write the following statements in symbolic form

Even though it is not cloudy, it is still raining


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


Choose the correct alternative:

A biconditional statement is the conjunction of two ______ statements


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 symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)


If q: There are clouds in the sky then p: it is raining. The symbolic form is ______


If p and q are true and rands are false statements, then which of the following is true?


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


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


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


The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______ 


Let S be a non-empty subset of R. Consider the following statement:

p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p? 


The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______ 


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


Using the statements

p: Seema is fat,

q: Seema is happy,

Write the following statements in symbolic form;

  1. Seema is thin and happy.
  2. If Seema is fat then she is unhappy.

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