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

Write the truth value of the negation of the following statement. 5 is an irrational number.

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प्रश्न

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

`sqrt5` is an irrational number.

एका वाक्यात उत्तर
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उत्तर

Truth value of the given statement is T.

∴ Truth value of its negation is F.

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पाठ 1: Mathematical Logic - Exercise 1.3 [पृष्ठ ७]

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संबंधित प्रश्‍न

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


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


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 ∧ r)]


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 following statement in symbolic form.

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


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 : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

~ (p ∨ q)


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q ∧ ~ p


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

Proof is lengthy and it is not 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.

Kanchanganga is in India and Everest is in Nepal.


Assuming the following statement.

p : Stock prices are high.

q : Stocks are rising.

to be true, find the truth value of the following.

Stock prices are high or stocks are not rising iff stocks are rising.


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


Write the negation of the following statement.

∃ x ∈ A, such that x + 5 < 11.


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


Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively


If p, q are true statement and r is false statement, then which of the following statements is a true statement.


The negation of ∼s ∨ (∼r ∧ s) 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? 


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


Write the contrapositive of the inverse of the statement:

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


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.
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Using truth table prove that:

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


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


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