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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

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

[~(~p ∧ ~q)] v q


Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)


If p ∧ q is false and p ∨ q is true, then ______ is not true.


Construct the truth table of the following:

p → (q → p)


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

(p ∨ q) is T and (p ∧ q) is T


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

(p ∨ q) is T and (p ∨ q) → q is F


Write the following statement in symbolic form.

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


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


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.

It is not true that Ram is tall and handsome.


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 → r


Write the negation of the following.

Ramesh is intelligent and he is hard working.


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


Write the negation of p → q


Write the following statements in symbolic form.

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


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


If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______ 


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


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


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


Write the following statement in symbolic form.

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


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


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)


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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