मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following. ∃ x ∈ A such that x2 < 0 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∃ x ∈ A such that x2 < 0

बेरीज

उत्तर

There is no x ∈ A which satisfies x2 < 0. So the given statement is false, hence its truth value is F.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Exercise 1.3 [पृष्ठ १७]

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Write truth values of the following statements: ∃ n ∈ N such that n + 5 > 10.


Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.


State which of the following is the statement. Justify. In case of a statement, state its truth value.

5 + 4 = 13


State which of the following is the statement. Justify. In case of a statement, state its truth value.

x – 3 = 14


State which of the following is the statement. Justify. In case of a statement, state its truth value.

Zero is a complex number.


State which of the following is the statement. Justify. In case of a statement, state its truth value.

Please get me breakfast.


State which of the following is the statement. Justify. In case of a statement, state its truth value.

All real numbers are whole numbers.


State which of the following is the statement. Justify. In case of a statement, state its truth value.

It rains heavily.


Write the truth values of the following.

4 is odd or 1 is prime.


Write the truth value of the following.

Milk is white if and only if sky is blue.


If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(p → q) ∧ ∼ r


If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:

(∼ r ↔ p) → ∼ q


If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.

∀ x ∈ A, x2 + x is an even number


Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

π is an irrational number.


Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

India is a country and Himalayas is a river.


`sqrt5` is an irrational but `3sqrt5` is a complex number.


Write the truth value of the following statement:

∀ n ∈ N, n + 6 > 8.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

The sum of interior angles of a triangle is 180°


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

`sqrt(-4)` is an irrational number.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

Did you eat lunch yet?


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

(x + y)2 = x2 + 2xy + y2 for all x, y ∈ R. 


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

Every real number is a complex number.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

1 is a prime number.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

3 + 5 > 11


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

The number π is an irrational number.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

The number 2 is the only even prime number.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

The number of arrangements of 7 girls in a row for a photograph is 7!.


State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.

Give me a compass box.


Which of the following is not a statement?


Choose the correct alternative :

For the following three statements
p : 2 is an even number.
q : 2 is a prime number.
r : Sum of two prime numbers is always even.
Then, the symbolic statement (p ∧ q) → ∼ r means.


Choose the correct alternative :

The statement (∼ p ∧ q) ∨∼ q is


Choose the correct alternative:

Which of the following is always true?


Choose the correct alternative :

If p is the sentence ‘This statement is false’ then


Fill in the blanks :

p ↔ q is false when p and q have ––––––––– truth values.


Fill in the blanks :

Truth value of 2 + 3 = 5 if and only if − 3 > − 9 is –––––––––.


State whether the following statement is True or False :

Dual of (p ∧ ∼ q) ∨ t is (p ∨ ∼ q) ∨ C.


State whether the following statement is True or False :

p ∧ t = p.


Solve the following :

State which of the following sentences are statements in logic.
Read a lot to improve your writing skill.


Solve the following :

State which of the following sentences are statements in logic.
(a + b)2 = a2 + 2ab + b2 for all a, b ∈ R.


Solve the following :

State which of the following sentences are statements in logic.
If x is real number then x2 ≥ 0.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

Please carry out my instruction.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

The Himalayas is the highest mountain range.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

(x − 2) (x − 3) = x2 − 5x + 6 for all x∈R.


Which of the following sentence is a statement? In case of a statement, write down the truth value.

What are the causes of rural unemployment?


Which of the following sentence is a statement? In case of a statement, write down the truth value.

0! = 1


Determine the truth value of the following statement.

x + y = 0 is the equation of a straight line if and only if y2 = 4x is the equation of the parabola.


Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.

If stock prices are high then stocks are not rising.


If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.

∼ (p ∧ q) → ∼ (q ∧ p)


If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.

∀ x ∈ A, x2 + 2 ≥ 5.


Which of the following statement is true


State the truth Value of x2 = 25


State the truth value of (p ˅ ∼p)


Choose the correct alternative :

Which of the following is not a statement?


The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.


State whether the following statement is True or False:

p ↔ q is false when p and q have different truth values


State whether the following statement is True or False:

Mathematical identities are true statements


The truth value of negation of “London is in England” is ______


If p ↔ q and p → q both are true, then find truth values of the following with the help of activity

p ˅ q

p ↔ q and p → q both are true if p and q has truth value `square`, `square` or `square`, `square`.

p ˅ q

i. If both p and q are true, then p ˅ q = `square` ˅ `square` = `square`

ii. If both p and q are false, then p ˅ q = `square` ˅ `square` = `square`


If p ↔ q and p → q both are true, then find truth values of the following with the help of activity

p ˄ q

p ↔ q and p → q both are true if p and q has truth value `square`, `square` or `square`, `square`

p ˄ q

i. If both p and q are true, then p ˄ q = `square` ˄ `square` = `square`

ii. If both p and q are false, then p ˄ q = `square` ˄ `square` = `square`


Which of the following quantified statement is true?


Let a: ~ (p ∧ ~ r) v (~ q v s) and

b: (p v s) ↔ (q ∧ r).

If the truth values of p and q are true and that of rands are false, then the truth values of a and bare respectively.


If the truth value of statement (q ∧ ~ r) → p is false (F), then the truth values of the statements p, q, rare respectively.


If p ↔ (~ p → q) is false, then the truth values of p and q are respectively ______.


If truth values of p ↔ r, r, p ↔ q are F, T, F respectively, then respective truth values of p and q are ______.


Using truth table prove that:

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`


Find the truth value of the following compound statement:

5 + 4 = 9 and 6 × 3 = 12


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×