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

Write the truth value of the following. 4 is odd or 1 is prime. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Write the truth values of the following.

4 is odd or 1 is prime.

बेरीज

उत्तर

Let p: 4 is odd.
      q: 1 is prime.
Then the symbolic form of the given statement is p∨q.
The truth values of both p and q are F.
∴ The truth value of p∨q is F ........[F∨F ≡ 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

If p ˄ q = F, p → q = F, then the truth value of p and q is ______.


Write the following statement in symbolic form and find its truth value:
∀ n ∈ N, n2 + n is an even number and n2 - n is an odd number.


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.

Please get me breakfast.


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

Congruent triangles are similar.


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

All real numbers are whole numbers.


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

Can you speak in Marathi?


Write the truth value of the following.

Milk is white if and only if sky is blue.


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:

(∼ 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 → p) → (∼ s ∨ r)]


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

∃ x ∈ A such that x – 8 = 1


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


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.

(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.

The number π 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.

Bring the motor car here.


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 :

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 :

If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is


The negation of the proposition “If 2 is prime, then 3 is odd”, is ______ 


Choose the correct alternative :

If p is the sentence ‘This statement is false’ then


Choose the correct alternative :

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


If p ∨ q is true then truth value of ∼ p ∨ ∼ 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 :

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 :

Dual of “John and Ayub went to the forest” is “John and Ayub went to the forest”.


State whether the following statement is True or False :

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


State whether the following statement is True or False :

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


Solve the following :

State which of the following sentences are statements in logic.
(a + b)2 = a2 + 2ab + b2 for all a, b ∈ R.


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.
Do not come inside the room.


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.


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

Please carry out my instruction.


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

0! = 1


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 not high or stocks are rising.


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

p ↔ (q → ∼ p)


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

∼ (p ∧ q) → ∼ (q ∧ p)


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

∃ x ∈ A, such that 3x + 2 > 9


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

∃ x ∈ A, such that x + 3 < 11.


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)


State whether the following statement is True or False:

Truth value of `sqrt(3)` is not an irrational number is F


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


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


Without using truth table show that

(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)


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`


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 ______.


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.


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×