हिंदी

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)

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) ↔ ~(p ∨ q)

योग
Advertisements

उत्तर

(p → q) ↔ ~(p ∨ q) ≡ (T → T) ↔ (T ∨ T)

≡ T ↔ ~ T

≡ T ↔ F

≡ F

Hence, truth value if F.

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 3.4 | पृष्ठ ११

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

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


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


Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p


Construct the truth table of the following:

p → (q → p)


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) → q is F


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

(p ∧ q) is F and (p ∧ q) → q is T


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.

All men are animals.


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 ∧ r)


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)]


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.

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


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

It is not true that Ram is tall and handsome.


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 ∧ 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) ∧ r


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.

I will have tea or coffee.


If q: There are clouds in the sky then p: it is raining. The symbolic form is ______


Which of the following is false?


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? 


The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______ 


Write the following statement in symbolic form.

It is not true that `sqrt(2)` is a rational number.


If a statement b has truth value False and \[(p\wedge q)\leftrightarrow r\] has truth value True, then which of the following has truth value True?


Let p: I am brave.
      q: I will climb the Mount Everest.

The symbolic form of a statement,

‘I am neither brave nor I will climb the mount Everest’ is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×