हिंदी

Construct the truth table of the following statement pattern. (p ∧ q) ↔ (q ∨ r)

Advertisements
Advertisements

प्रश्न

Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (q ∨ r)

सारिणी
Advertisements

उत्तर

p q r p ∧ q q ∨ r (p ∧ q) ↔ (q ∨ r)
T T T T T T
T T F T T T
T F T F T F
T F F F F T
F T T F T F
F T F F T F
F F T F T F
F F F F F T
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Exercise 1.2 [पृष्ठ १३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.2 | Q 1.03 | पृष्ठ १३

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

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


Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls


Evaluate: ∫ x . log x dx


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.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Write the following compound statement symbolically.

The angle is right angle if and only if it is of measure 90°.


Write the following compound statement symbolically.

Angle is neither acute nor obtuse.


Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]


Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]


Construct the truth table of the following:

∼ (∼p ∧ ∼q) ∨ q


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

(p ∨ q) is T and (p ∧ q) is T


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Write the negation of the following statement.

2 + 3 ≠ 5


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.


Find the truth value of the following statement.

3 is a prime number and an odd number.


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

[(p ∨ s) → r] ∨ ~ [~ (p → q) ∨ s]


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

~ (p ∨ q)


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.

3 is prime number if 3 is perfect square number.


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

It is not true that intelligent persons are neither polite nor helpful.


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


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.

7 is prime number and Tajmahal is in Agra.


A biconditional statement is the conjunction of two ______ statements.


The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


Write the following statement in symbolic form:

Milk is white if and only if the sky is not blue.


Write the following statements in symbolic form

Even though it is not cloudy, it is still raining


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


Write the negation of p → q


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


State whether the following statement is True or False:

The converse of inverse of ~ p → q is q → ~ p


If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.


If p, q are true statement and r is false statement, then which of the following statements is a true statement.


Which of the following is false?


The inverse of the statement "If its quality is good. then it is expensive.", is ______ 


The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______ 


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? 


Which of the following is logically equivalent to `∼(∼p \implies q)`?


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


Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka


Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.


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×