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

Assuming the first statement p and second as q. Write the following statement in symbolic form. The Sun has set and Moon has risen.

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प्रश्न

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

The Sun has set and Moon has risen.

बेरीज
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उत्तर

Let p : The sun has set.
q : The moon has risen

The symbolic form is p ∧ q.

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पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३१]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.03 | पृष्ठ ३१

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


Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls


Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (q ∨ r)


Construct the truth table of the following statement pattern.

(q → p) ∨ (∼ p ↔ q)


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


Write the negation of the following statement.

− 3 is a natural number.


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.

For every x ∈ N, x + 3 < 8.


Write the following statement in symbolic form.

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


Write the following statement in symbolic form.

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


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

p ∧ (q ∧ r)


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)


Fill in the blanks :

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


Negation of “some men are animal” is ______.


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 → 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


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


Write the negation of the following statement.

I will have tea or coffee.


Negation of p → (p ˅ ∼ q) is ______


Write the following statements in symbolic form

Even though it is not cloudy, it is still raining


If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.


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


Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."


Conditional of p → q is equivalent to p → ∼ q.


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


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

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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