हिंदी

If p and q are true and r and s are false, find the truth value of the following compound statement. (p → q) ∨ (r ∧ s)

Advertisements
Advertisements

प्रश्न

If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ∨ (r ∧ s) 

योग
Advertisements

उत्तर

(p → q) ∨ (r ∧ s) ≡ (T → T) ∨ (F ∧ F) 

≡ T ∨ F

≡ T
Hence, truth value if T.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Exercise 1.4 [पृष्ठ ११]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.4 | Q 3.2 | पृष्ठ ११

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p


Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p


Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]


Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ q)]


Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∧ q) is T


Write the truth value of the following statement.

16 is an even number and 8 is a perfect square.


Write the truth value of the negation of the following statement.

`sqrt5` is an irrational number.


Write the following statement in symbolic form.

Even though it is not cloudy, it is still raining.


Write the following statement in symbolic form.

If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.


Find the truth value of the following statement.

It is not true that 3 − 7i is a real number.


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ↔ ~(p ∨ q)


Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

Sunday is a holiday and Ram studies on holiday.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement:

p ↔ ~ q


Assuming the first statement p and second as q. Write the following statement in symbolic form.

Even though it is not cloudy, it is still raining.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

It is not true that the proof is lengthy but it is interesting.


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → r


Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ p ∨ q


Rewrite the following statement without using the connective ‘If ... then’.

If 10 − 3 = 7 then 10 × 3 ≠ 30.


Consider the following statements.

  1. If D is dog, then D is very good.
  2. If D is very good, then D is dog.
  3. If D is not very good, then D is not a dog.
  4. If D is not a dog, then D is not very good. 

Identify the pairs of statements having the same meaning. Justify.


Write the negation of the following statement.

∀ n ∈ N, n + 3 > 9.


The negation of (p ∨ ∼q) ∧ q is ______


Which of the following is NOT true for p → q.


The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______


Converse of the statement q `rightarrow` p is ______.


The statement ∼(p ↔ ∼q) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×