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

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

Advertisements
Advertisements

प्रश्न

Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]

तक्ता
Advertisements

उत्तर

p q ∼ p ∼ q p ∨ ∼ q (p ∨ ∼ q) ∧ q ∼ p ∧ [(p ∨ ∼ q) ∧ q]
T T F F T T F
T F F T T F F
F T T F F F F
F F T T T F F
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

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


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 ∧ r)]


Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ q)]


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.

Even though it is cloudy, it is still raining.


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


Write the truth value of the following statement.

16 is an even number and 8 is a perfect square.


Write the negation of the following statement.

All men are animals.


Write the negation of the following statement.

− 3 is a natural number.


Write the negation of the following statement.

2 + 3 ≠ 5


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

`sqrt5` is an irrational number.


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

London is in England.


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

For every x ∈ N, x + 3 < 8.


Fill in the blanks :

Conjunction of two statement p and q is symbolically written as ______.


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.

To be brave is necessary and sufficient condition to climb the Mount Everest.


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

The drug is effective though it has side effects.


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.


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.

If proof is lengthy then it is interesting.


Write the negation of the following.

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


Write the negation of the following.

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


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 following statements in symbolic form

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


Choose the correct alternative:

A biconditional statement is the conjunction of two ______ statements


State whether the following statement is True or False:

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


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


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


If p and q are true and rands are false statements, then which of the following is true?


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


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


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


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


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: ______ 


Write the following statement in symbolic form.

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


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×