हिंदी

If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement. ∀ x ∈ A, x2 + 2 ≥ 5. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

∀ x ∈ A, x2 + 2 ≥ 5.

योग
Advertisements

उत्तर

∀ x ∈ A, x2 + 2 ≥ 5.

x = 2; 22 + 2 ≥ 5

∵ for all given values of

x = 2, 3, 4, 5, 6, 7, 8

x2 + 2 ≥ 5 condition satisfied.

∴ The truth value of the given statement is True (T).

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३४]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.21 | पृष्ठ ३४

संबंधित प्रश्न

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.

Zero is a complex number.


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

All real numbers are whole numbers.


Write the truth values of the following.

24 is a composite number or 17 is a prime number.


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

(q ∧ r) ∨ (∼ p ∧ s)


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

∀ x ∈ A, 2x + 9 > 14


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.


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

Please get me a glass of water.


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

cos2θ − sin2θ = cos2θ for all θ∈R.


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.

`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.

Have a cup of cappuccino.


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


Which of the following statements is false?


Choose the correct alternative :

The statement (∼ p ∧ q) ∨∼ q is


Fill in the blanks :

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


State whether the following statement is True or False :

p ∨ q has truth value F is both p and q has truth value F.


Solve the following :

State which of the following sentences are statements in logic.
(2 + 1)2 = 9.


Solve the following :

State which of the following sentences are statements in logic.
How beautiful the flower is!


Solve the following :

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


Solve the following :

State which of the following sentences are statements in logic.
Do not come inside the room.


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

Every parallelogram is a rhombus.


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.


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

(p ∧ q) → ∼ p.


State the truth Value of x2 = 25


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


The truth value of the statement “Neither 27 is a prime number nor divisible by 4” 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`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×