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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

उत्तर

p ˄ (~p ˄ q)

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पाठ 1.1: Mathematical Logic - Q.1

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)


Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (q ∨ r)


Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]


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) ∨ r] ∧ [∼r ∨ (p ∧ q)]


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.

I like playing but not singing.


Express the following statement in symbolic form.

Even though it is cloudy, it is still raining.


Write the truth value of the following statement.

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


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 negation of the following statement.

All men are animals.


Write the negation of the following statement.

2 + 3 ≠ 5


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

London is in England.


Write the following statement in symbolic form.

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


Write the following statement in symbolic form.

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


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.

If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.


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.

If Sunday is not holiday then Ram studies on holiday.


Fill in the blanks :

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


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.

Kavita is brilliant and brave.


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

x3 + y3 = (x + y)3 if xy = 0.


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.

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 the connective ‘If ... then’.

If 10 − 3 = 7 then 10 × 3 ≠ 30.


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


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the following statements in symbolic form

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


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


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)


Negation of “Some men are animal “ is ______


Write the following statements in symbolic form.

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


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?


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


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


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


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


Which of the following is logically equivalent to `∼(∼p \implies q)`?


Converse of the statement q `rightarrow` p is ______.


Write the following statement in symbolic form.

It is not true that `sqrt(2)` is a rational number.


The statement ∼(p ↔ ∼q) is ______.


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


From the following set of statements, select two statements which have similar meaning.

  1. If a man is judge, then he is honest.
  2. If a man is not a judge, then he is not honest.
  3. If a man is honest, then he is a judge.
  4. If a man is not honest, then he is not a judge.

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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