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

State which of the following is the statement. Justify. In case of a statement, state its truth value. All real numbers are whole numbers. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

All real numbers are whole numbers.

एका वाक्यात उत्तर

उत्तर

It is a statement which is false, hence its truth value is ‘F’.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Exercise 1.1 [पृष्ठ ७]

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.


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.

Can you speak in Marathi?


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

The sum of cube roots of unity is zero.


Write the truth values of the following.

4 is odd or 1 is prime.


Write the truth values of the following.

5 is a prime number and 7 divides 94.


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:

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:

(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] ∨ [(q → p) → (∼ s ∨ r)]


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

∼ [(∼ p ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)


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

∀ x ∈ A, x2 + x is an even number


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

∃ x ∈ A such that x2 < 0


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:

4! = 24.


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:

Please get me a glass of water.


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


Write the truth value of the following statement:

∃ n ∈ N such that n + 5 > 10.


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.


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.

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.

1 ! = 0


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.


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

Two co-planar lines are either parallel or intersecting.


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

It may rain today.


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

If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 7.


Which of the following statements is false?


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 :

Conditional p → q is equivalent to


Choose the correct alternative :

Negation of the statement “This is false or That is true” is


Fill in the blanks :

Let p : the problem is easy. r : It is not challenging then verbal form of ∼ p → r is –––––––––.


State whether the following statement is True or False :

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


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 :

“His birthday is on 29th February” is not a statement.


Solve the following :

State which of the following sentences are statements in logic.
x + 3 = 8 ; x is variable.


Solve the following :

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


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.
Why are you sad?


Solve the following :

State which of the following sentences are statements in logic.
All integers are natural numbers.


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

The square of every real number is positive.


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.


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.

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


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

∼ [(p → q) ↔ (p ∧ ∼ q)]


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

∀ x ∈ A, x2 + 2 ≥ 5.


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


State the truth value of `sqrt(3)` is not an irrational number


State the truth value of (p ˅ ∼p)


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

~ p ∧ (q ∨ ~ r)


Choose the correct alternative :

Which of the following statement is true?


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) ˄ ~ p is a contradiction


State whether the following statement is True or False:

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


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


Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p


Given following statements
p: 9 × 5 = 45
q: Pune is in Maharashtra
r: 3 is the smallest prime number

Write truth values by activity

i) (p ˄ q) ˄ r = `(square` ˄ `square)` ˄ `square`

= `square` ˄ `square`

= `square`

ii) ~ ( p ˄ r ) = `~(square` ˄ `square)`

= `~ square`

= `square`

iii) p → q = `square → square`

= `square`


If (p ∧ ~ q) → ~ p is false, 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 ______.


If p `rightarrow` (p ∧ ∼q) is false, then the truth values of p and q are respectively ______.


If p : Every square is a rectangle. q : Every rhombus is a kite, then truth values of p `rightarrow` q and p `leftrightarrow` q are ______ and ______ respectively.


Using truth table prove that:

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×
Our website is made possible by ad-free subscriptions or displaying online advertisements to our visitors.
If you don't like ads you can support us by buying an ad-free subscription or please consider supporting us by disabling your ad blocker. Thank you.