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

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

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

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


Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.


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.

Zero is a complex number.


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 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.

It rains heavily.


Write the truth values of the following.

4 is odd or 1 is prime.


Write the truth values of the following.

5 is a prime number and 7 divides 94.


Write the truth value of the following.

If 3 × 5 = 8 then 3 + 5 = 15.


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:

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

∃ x ∈ A such that x2 < 0


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


Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:

π is an irrational number.


Write the truth value of the following statement:

∃ n ∈ N such that n + 5 > 10.


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.

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.

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.

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.

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.

Two co-planar lines are either parallel or intersecting.


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

It may rain today.


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 :

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 :

The statement (∼ p ∧ q) ∨∼ q is


Fill in the blanks :

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


If p ∨ q is true then truth value of ∼ p ∨ ∼ q is ______.


Fill in the blanks :

Truth value of if x = 2, then x2 = − 4 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 :

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 :

p ∧ t = p.


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.
Why are you sad?


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.
All integers are natural numbers.


Solve the following :

State which of the following sentences are statements in logic.
If x is real number then x2 ≥ 0.


Solve the following :

State which of the following sentences are statements in logic.
What a horrible sight it was!


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.

The Himalayas is the highest mountain range.


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

(x − 2) (x − 3) = x2 − 5x + 6 for all x∈R.


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?


Determine the truth value of the following statement.

If 9 > 1 then x2 − 2x + 1 = 0 for x = 1


Determine the truth value of the following statement.

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


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

∃ x ∈ A, such that x + 3 < 11.


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


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


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`


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`


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


If the truth value of statement (q ∧ ~ r) → p is false (F), then the truth values of the statements p, q, rare respectively.


If p ↔ (~ p → q) is false, then the truth values of p and q are respectively ______.


If p `rightarrow` (p ∧ ∼q) is false, 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)`.


Using truth table prove that:

`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`


Find the truth value of the following compound statement:

5 + 4 = 9 and 6 × 3 = 12


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×