हिंदी

If p and q are true and r and s are false, find the truth value of the following compound statement. ~ [(~ p ∨ s) ∧ (~ q ∧ r)] - Mathematics and Statistics

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 ∨ s) ∧ (~ q ∧ r)]

योग

उत्तर

~ [(~ p ∨ s) ∧ (~ q ∧ r)] ≡ ~[(~T ∨ F) ∧ (~T ∧ F)]

≡ ~[(F ∨ F) ∧ (F ∧ F)

≡ ~ (F ∧ F)

≡ ~ 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] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.4 | Q 3.3 | पृष्ठ ११

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).


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 converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.


Write the following compound statement symbolically.

Angle is neither acute nor obtuse.


If p ∧ q is false and p ∨ q is true, then ______ is not true.


Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)


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

(p ∨ q) is T and (p ∧ q) is T


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

(p ∨ q) is T and (p ∨ q) → q is F


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


Write the negation of the following statement.

2 + 3 ≠ 5


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

London is in England.


Write the following statement in symbolic form.

If triangle is equilateral then it is equiangular.


Write the following statement in symbolic form.

It is not true that “i” is a real number.


Write the following statement in symbolic form.

Stock prices are high if and only if stocks are rising.


Write the following statement in symbolic form.

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


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) 


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q ∧ ~ p


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

The Sun has set and Moon has risen.


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

If a real number is not rational, then it must be irrational.


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

Proof is lengthy and it is not interesting.


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

It is interesting iff the proof is lengthy.


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) ∨ 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


Write the negation of the following.

Ramesh is intelligent and he is hard working.


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


Negation of p → (p ˅ ∼ q) is ______


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


Write the following statements in symbolic form

Even though it is not cloudy, it is still raining


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


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


Let S be a non-empty subset of R. Consider the following statement:

p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p? 


Write the following statement in symbolic form.

4 is an odd number if 3 is not a prime factor of 6.


If p, q are true statements and r, s are false statements, then write the truth value of the compound statement

(p `→` ∼ r) `→` (q ∧ s)


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×