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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

State the truth value of (p ˄ ∼p) - Mathematics and Statistics

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प्रश्न

State the truth value of (p ˄ ∼p) 

तक्ता
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उत्तर

p ∼p p ∧ ∼p
T F F
F T F

 Truth value of  (p ˄ ∼p) is F.

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पाठ 1.1: Mathematical Logic - Very Short Answers

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

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.

A quadratic equation cannot have more than two roots.


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.

5 is a prime number and 7 divides 94.


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

∀ x ∈ A, 2x + 9 > 14


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


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:

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


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 − 6x + 8 = 0 implies x = −4 or x = −2.


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.

Have a cup of cappuccino.


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.

3 + 5 > 11


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.


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.


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.


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


If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.


Choose the correct alternative :

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


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 :

p ↔ q is false when p and q have ––––––––– truth values.


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.
Read a lot to improve your writing skill.


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.
What a horrible sight it was!


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.


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

∃ x ∈ A, such that x + 3 < 11.


Which of the following statement is true


Choose the correct alternative :

Which of the following statement is true?


State whether the following statement is True or False:

p ↔ q is false when p and q have different truth values


State whether the following statement is True or False:

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


State whether the following statement is True or False:

Mathematical identities are true statements


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


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


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`


Which of the following quantified statement is true?


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?


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