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

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

प्रश्न

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

∀ x ∈ A, x2 < 18.

बेरीज

उत्तर

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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३४]

APPEARS IN

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

संबंधित प्रश्‍न

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

x – 3 = 14


If p ∧ q is F, p → q is F then the truth values of p and q are ________.


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.


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


Write the truth value of the following statement:

∀ n ∈ N, n2 + n is even number while n2 – n is an odd number.


Write the truth value of the following statement:

The square of any even number is odd or the cube of any odd number is odd.


Write the truth value of the following statement:

In ΔABC if all sides are equal then its all angles are equal.


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

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


Choose the correct alternative :

Which of the following is an open statement?


State whether the following statement is True or False :

There are 24 months in year is a statement.


Solve the following :

State which of the following sentences are statements in logic.
z is a positive number.


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.

a2 − b2 = (a + b) (a − b) for all a, b ∈ R.


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

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


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

∃ x ∈ A, such that 3x + 2 > 9


State whether the following statement is True or False:

The dual of (p ˄ q) ˅ ~ q is (p ˅ q) ˄ ~ q


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×