मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

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)

तक्ता
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
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Exercise 1.2 [पृष्ठ १३]

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्‍न

Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


Write the following compound statement symbolically.

Angle is neither acute nor obtuse.


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 ∧ p)


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.


Express the following statement in symbolic form.

I like playing but not singing.


Express the following statement in symbolic form.

Even though it is cloudy, it is still raining.


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

London is in England.


Write the following statement in symbolic form.

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


Write the following statement in symbolic form.

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


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.

If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.


Find the truth value of the following statement.

Neither 27 is a prime number nor divisible by 4.


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]


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.

q → p


Negation of “some men are animal” is ______.


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.

Kavita is brilliant and brave.


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

If Kiran drives the car, then Sameer will walk.


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

The necessary condition for existence of a tangent to the curve of the function is continuity.


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

If the question paper is not easy then we shall not pass.


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) ∧ r


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If demand falls, then price does not increase.


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


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


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


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


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.


Which of the following is false?


The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______


The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______


Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."


Conditional of p → q is equivalent to p → ∼ q.


Let p, q and r be any three logical statements. Which of the following is true?


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


Write the following statement in symbolic form.

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


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’.


From the following set of statements, select two statements which have similar meaning.

  1. If a man is judge, then he is honest.
  2. If a man is not a judge, then he is not honest.
  3. If a man is honest, then he is a judge.
  4. If a man is not honest, then he is not a judge.

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)


Using truth table prove that:

~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×