हिंदी

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 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

योग
Advertisements

उत्तर

Truth values of p and q are T and truth values of r and s are F.

(p → q) ∧ (∼ r) ≡ (T → T) ∧ (∼ F)
                         ≡ T ∧ T ≡ T
Hence the truth value of the given statement is true.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Exercise 1.1 [पृष्ठ ७]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.1 | Q 4.4 | पृष्ठ ७

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


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.

The sunsets in the west


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.

5 is a prime number and 7 divides 94.


Write the truth values of the following.

It is not true that 5−3i is a real number.


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 ∧ 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.


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

∃ x ∈ A such that 3x + 8 > 40


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.


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.


Write the truth value of the following statement:

∀ n ∈ N, n + 6 > 8.


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.

Did you eat lunch yet?


Which of the following is not a statement?


Choose the correct alternative :

Which of the following is an open statement?


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


Choose the correct alternative :

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


Fill in the blanks :

The statement q → p is called as the ––––––––– of the statement p → q.


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.
Read a lot to improve your writing skill.


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!


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.

4 + 5 = 7 or 9 − 2 = 5


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.

Stock prices are high and stocks are rising if and only if 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, 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 (p ˅ ∼p)


Choose the correct alternative :

Which of the following statement is true?


State whether the following statement is True or False:

p → q is equivalent to p → ~ q


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`


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.


The position vector of points A and B are `6bar(a) + 2bar(b) and bar(a) -3bar(b)` . If the point C divides AB in the ratio 3 : 2 then show that the position vector of C is 3`bar(a)- bar(b)`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×