English

If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement. ∀ x ∈ A, x2 < 18. - Mathematics and Statistics

Advertisements
Advertisements

Question

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

∀ x ∈ A, x2 < 18.

Sum
Advertisements

Solution

For x = 5, x2 = 52 = 25 < 18

∴ x = 5 does not satisfies the equation x2 < 18.

∴ The given statement is false.

∴ Its truth value is F.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 34]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.21 | Page 34

RELATED QUESTIONS

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.

Close the door.


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

It rains heavily.


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 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 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:

If x is a whole number then x + 6 = 0.


Write the truth value of the following statement:

∃ n ∈ N such that n + 5 > 10.


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

A triangle has ‘n’ sides.


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

You are amazing!


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

He is an actor.


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.

Give me a compass box.


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 :

∼ (p ∨ q) ∨ (∼ p ∧ q) is logically equivalent to


If p ∨ q is true then truth value of ∼ p ∨ ∼ q is ______.


Fill in the blanks :

Truth value of if x = 2, then x2 = − 4 is –––––––––.


State whether the following statement is True or False :

Truth value of 2 + 3 < 6 is F.


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.
Do not come inside the room.


Determine the truth value of the following statement.

If 9 > 1 then x2 − 2x + 1 = 0 for x = 1


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

∼ [(p → q) ↔ (p ∧ ∼ q)]


State whether the following statement is True or False:

p ˅ ~ p ≡ ~ c


Which of the following quantified statement is true?


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×