English

Determine the truth value of the following statement. If 9 > 1 then x2 − 2x + 1 = 0 for x = 1 - Mathematics and Statistics

Advertisements
Advertisements

Question

Determine the truth value of the following statement.

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

Sum
Advertisements

Solution

Let p : 9 > 1
q : x2 – 2x + 1 = 0 for x = 1 

The truth values of p and q are T and T respectively. The given statement in symbolic form is p → q.

∴ p → q ≡ T → T ≡ T

∴ Truth value of the given statement is T.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 32]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.06 | Page 32

RELATED QUESTIONS

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

Do you like Mathematics?


Write the truth values of the following.

It is not true that 5−3i is a real number.


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:

(∼ r ↔ p) → ∼ q


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)] ∨ [(q ∧ r) ∨ (p ∧ r)]


If A = {1, 2, 3, 4, 5} then which of the following is not true?


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.


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.

Can you speak in English?


Choose the correct alternative :

Which of the following is an open statement?


Choose the correct alternative :

The statement (∼ p ∧ q) ∨∼ q is


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 :

Truth value of 2 + 3 < 6 is F.


State whether the following statement is True or False :

Truth value of `sqrt(5)` is not an irrational number is T.


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?


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

It is false that stocks are rising and stock prices are high.


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

∀ x ∈ A, x2 < 18.


If p is any statement then ( p ˅ ∼ p) is a


If statements p, q are true and r, s are false, determine the truth values of the following.

~ p ∧ (q ∨ ~ r)


If statements p, q are true and r, s are false, determine the truth values of the following.

(p ∧ ~r) ∧ (~q ∨ s)


State whether the following statement is True or False:

p → q is equivalent to p → ~ q


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.


If q Λ ∼p is T, then which of the following is correct?


Consider the following two statements.

Statement p:

The value of sin 120° can be divided by taking θ = 240° in the equation 2 sin `θ/2` = `sqrt(1 + sin θ) - sqrt(1 - sinθ)`.

Statement q:

The angles A, B, C and D of any quadrilateral ABCD satisfy the equation `cos(1/2(A + C)) + cos(1/2(B + D))` = 0

Then the truth values of p and q are respectively.


Using truth table prove that:

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×