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

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 :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.


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.

Congruent triangles are similar.


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

x2 = x


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.


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

It rains heavily.


Write the truth values of the following.

4 is odd or 1 is prime.


Write the truth values of the following.

64 is a perfect square and 46 is a prime number.


Write the truth value of the following.

Milk is white if and only if sky is blue.


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:

[∼ p ∧ (∼ q ∧ r)] ∨ [(q ∧ r) ∨ (p ∧ 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 such that x2 < 0


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

∀ x ∈ A, 2x + 9 > 14


Write the truth value of the following statement:

∀ n ∈ N, n2 + n is even number while n2 – n is an odd number.


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.

You are amazing!


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.

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.

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:

Which of the following is always true?


Choose the correct alternative :

∼ (p ∨ q) ∨ (∼ p ∧ q) is logically equivalent to


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


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

There are 24 months in year is a statement.


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.
(a + b)2 = a2 + 2ab + b2 for all a, b ∈ R.


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.
The square of any odd number is even.


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.


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

Every parallelogram is a rhombus.


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?


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

0! = 1


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

The quadratic equation ax2 + bx + c = 0 (a ≠ 0) always has two real roots.


Determine the truth value of the following statement.

It is not true that 2 + 3 = 6 or 12 + 3 =5


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 ∧ q)


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

∀ x ∈ A, x2 < 18.


Which of the following statement is true


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


State the truth Value of x2 = 25


State the truth value of (p ˄ ∼p) 


State whether the following statement is True or False:

p → q is equivalent to p → ~ q


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:

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


State whether the following statement is True or False:

Mathematical identities are true statements


State whether the following statement is True or False:

p ˅ ~ p ≡ ~ c


The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______


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


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 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`


Let a: ~ (p ∧ ~ r) v (~ q v s) and

b: (p v s) ↔ (q ∧ r).

If the truth values of p and q are true and that of rands are false, then the truth values of a and bare respectively.


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


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.


lf p, q are true statements and r, s are false statements, then find the truth value of ∼ (p ∧ ∼r) ∨ (∼q ∨ s).


Using truth table prove that:

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×