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

Choose the correct alternative: Negation of p → (p ˅ ~q) is - Mathematics and Statistics

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प्रश्न

Choose the correct alternative:

Negation of p → (p ˅ ~q) is

पर्याय

  • ~p → (~p ˅ q)

  • p ˄ (~p ˄ q)

  • ~p ˅ (~p ˅ ~q)

  • ~p → (~p → q)

MCQ
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उत्तर

p ˄ (~p ˄ q)

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पाठ 1.1: Mathematical Logic - Q.1

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


Write the following compound statement symbolically.

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


Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (q ∨ r)


Construct the truth table of the following statement pattern.

(p ∨ ∼ q) → (r ∧ p)


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

(p ∧ q) is F and (p ∧ q) → q is T


Express the following statement in symbolic form.

Even though it is cloudy, it is still raining.


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.

16 is an even number and 8 is a perfect square.


Write the negation of the following statement.

− 3 is a natural number.


Write the negation of the following statement.

2 + 3 ≠ 5


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.

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


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.


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


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) ∧ ∼ r


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 following statements in symbolic form

Even though it is not cloudy, it is still raining


State whether the following statement is True or False:

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


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.


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


If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.


Write the contrapositive of the inverse of the statement:

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


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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