हिंदी

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 - 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:

(∼ r ↔ p) → ∼ q

योग
Advertisements

उत्तर

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

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

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 4.5 | पृष्ठ ७

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.

x2 = x


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.

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 → s)


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


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:

4! = 24.


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


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.


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

`sqrt(-4)` 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.

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.

1 is a prime number.


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.

If a + b < 7, where a ≥ 0 and b ≥ 0 then a < 7 and b < 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?


Which of the following statements is false?


Choose the correct alternative :

The statement (∼ p ∧ q) ∨∼ q is


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


Fill in the blanks :

Truth value of if x = 2, then x2 = − 4 is –––––––––.


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 :

There are 24 months in year is a statement.


State whether the following statement is True or False :

p ∨ q has truth value F is both p and q has truth value F.


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 :

“His birthday is on 29th February” is not a statement.


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.
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.

Please carry out my instruction.


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


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 3x + 2 > 9


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

∀ x ∈ A, x2 + 2 ≥ 5.


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


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

(p ∧ ~r) ∧ (~q ∨ s)


State whether the following statement is True or False:

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


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


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


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×