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

Construct the truth table of the following statement pattern. p → [∼ (q ∧ r)] - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]

तक्ता
Advertisements

उत्तर

p q r q ∧ r ∼ (q ∧ r) p → [∼ (q ∧ r)]
T T T T F F
T T F F T T
T F T F T T
T F F F T T
F T T T F T
F T F F T T
F F T F T T
F F F F T 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 [2]

संबंधित प्रश्‍न

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


Write the following compound statement symbolically.

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


Construct the truth table of the following statement pattern.

[p → (q → r)] ↔ [(p ∧ q) → r]


Construct the truth table of the following:

[(p ∧ q) ∨ r] ∧ [∼r ∨ (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.

The Himalayas are the highest mountains but they are part of India in the North East.


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.

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


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.

Neither 27 is a prime number nor divisible by 4.


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 ∧ (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) → 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 not holiday or Ram studies on holiday.


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.

~ (p ∨ q)


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.

It is not true that Ram is tall and handsome.


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


Write the negation of the following.

If ∆ABC is not equilateral, then it is not equiangular.


Write the negation of the following.

Ramesh is intelligent and he is hard working.


Assuming the following statement.

p : Stock prices are high.

q : Stocks are rising.

to be true, find the truth value of the following.

Stock prices are high or stocks are not rising iff stocks are rising.


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.


Write the negation of the following statement.

10 > 5 and 3 < 8


Write the negation of the following statement.

I will have tea or coffee.


A biconditional statement is the conjunction of two ______ statements.


If p → q is an implication, then the implication ∼ q → ∼ p is called its


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


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


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)


Without using truth table show that -

(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra


If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.


Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively


The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)


The statement, 'If I go to school, then I will get knowledge' is equivalent to ______ 


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


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


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×