हिंदी

If statements p, q are true and r, s are false, determine the truth values of the following. ~ p ∧ (q ∨ ~ r) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

~ p ∧ (q ∨ ~ r)

योग
Advertisements

उत्तर

~ p ∧ (q ∨ ~ r)

≡ ∼T ∧ (T ∨ ∼ F)

≡ F ∧ (T ∨ T)

≡ F ∧ T

≡ F

∴ Truth value of ~ p ∧ (q ∨ ~ r) is F

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.1: Mathematical Logic - Short Answers I

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Write truth values of the following statements: ∃ n ∈ N such that n + 5 > 10.


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.

Close the door.


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

All real numbers are whole numbers.


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 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, x is an even number.


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:

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


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


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

Please grant me a loan.


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.

(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.

With the sunset the day ends.


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

The number 2 is the only even prime number.


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

The number of arrangements of 7 girls in a row for a photograph is 7!.


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?


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 :

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.


State whether the following statement is True or False :

x2 = 25 is true 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.
Read a lot to improve your writing skill.


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.
Do not come inside the room.


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.


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.

If stock prices are high then stocks are not rising.


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.


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) ↔ (p ∧ ∼ q)]


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


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


State the truth value of (p ˅ ∼p)


Choose the correct alternative :

Which of the following is not a statement?


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


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


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


The negation of 'For every real number x, `x^2 ≥ 0`' is ______ 


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.


Find the truth value of the following compound statement:

5 + 4 = 9 and 6 × 3 = 12


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×