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

Rewrite the following statement without using the connective ‘If ... then’. If it rains then the principal declares a holiday.

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प्रश्न

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

If it rains then the principal declares a holiday.

बेरीज
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उत्तर

Let p : It rains.

q : The principal declares a holiday.

The given statement is p → q.

But p → q ≡ ~p ∨ q.

∴ The given statement can be written as ‘It does not rain or the principal declares a holiday’.

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पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.17 | पृष्ठ ३३

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

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

[~(~p ∧ ~q)] v 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) ∧ q] → p


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Write the negation of the following statement.

It is false that Nagpur is capital of Maharashtra


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

For every x ∈ N, x + 3 < 8.


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ∨ (r ∧ s) 


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ↔ ~(p ∨ q)


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]


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.

The Sun has set and Moon has risen.


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.

The necessary condition for existence of a tangent to the curve of the function is continuity.


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.


Write the negation of the following.

If ∆ABC is not equilateral, then it is not equiangular.


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

If 10 − 3 = 7 then 10 × 3 ≠ 30.


Write the negation of the following statement.

10 > 5 and 3 < 8


Negation of p → (p ˅ ∼ q) is ______


Write the following statement in symbolic form:

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


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


The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)


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


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


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.

Using truth table prove that:

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


If a statement b has truth value False and \[(p\wedge q)\leftrightarrow r\] has truth value True, then which of the following has truth value True?


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