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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Write the negation of the following statement. All men are animals.

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प्रश्न

Write the negation of the following statement.

All men are animals.

एका वाक्यात उत्तर
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उत्तर

Some men are not animals.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Exercise 1.3 [पृष्ठ ७]

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संबंधित प्रश्‍न

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

[~(~p ∧ ~q)] v q


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


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


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:

[(∼p ∨ q) ∧ (q → r)] → (p → r)


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

London is in England.


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.

It is not true that “i” is a real number.


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]


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 Sun has set and Moon has risen.


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.

It is not true that Ram is tall and handsome.


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

If proof is lengthy then it is interesting.


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


Write the negation of the following.

Ramesh is intelligent and he is hard working.


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

If 10 − 3 = 7 then 10 × 3 ≠ 30.


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.

∀ n ∈ N, n + 3 > 9.


Write the negation of p → q


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


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


If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.


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? 


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


Write the following statement in symbolic form.

4 is an odd number if 3 is not a prime factor of 6.


Write the contrapositive of the inverse of the statement:

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


Using truth table prove that:

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


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