हिंदी

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]

सारिणी

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
  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] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.2 | Q 1.05 | पृष्ठ १३

वीडियो ट्यूटोरियलVIEW ALL [2]

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


Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


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.

If Δ ABC is right-angled at B, then m∠A + m∠C = 90°


Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (q ∨ r)


Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]


Construct the truth table of the following statement pattern.

(∼ p → ∼ q) ∧ (∼ q → ∼ p)


Construct the truth table of the following statement pattern.

(q → p) ∨ (∼ p ↔ q)


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)]


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.

Milk is white or grass is green.


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 following statement.

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


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 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.


Write the following statement in symbolic form.

Even though it is not cloudy, it is still raining.


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.

Every accountant is free to apply his own accounting rules if and only if machinery is an asset.


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

p ∧ (q ∧ r)


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.


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.

If Sunday is not holiday then Ram studies on holiday.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

~ (p ∨ q)


Fill in the blanks :

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


Fill in the blanks :

Negation of “some men are animal” is –––––––––.


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.

x3 + y3 = (x + y)3 if xy = 0.


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.


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.


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.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

Proof is lengthy and it is not interesting.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

If proof is lengthy then it is interesting.


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.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

It is interesting iff the proof is lengthy.


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 → 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


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

If price increases, then demand falls.


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.

Ramesh is intelligent and he is hard working.


Write the negation of the following.

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


Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.


Rewrite the following statement without using the connective ‘If ... then’.

If 10 − 3 = 7 then 10 × 3 ≠ 30.


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.

I will have tea or coffee.


Write the negation of the following statement.

∀ n ∈ N, n + 3 > 9.


A biconditional statement is the conjunction of two ______ statements.


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


Find the negation of 10 + 20 = 30


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


Write the following statements in symbolic form

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


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


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


Negation of “Some men are animal “ is ______


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.


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


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


Which of the following is false?


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


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


The statement, 'If I go to school, then I will get knowledge' 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? 


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."


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)`?


If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.


Write the following statement in symbolic form.

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


The statement ∼(p ↔ ∼q) is ______.


Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


Write the contrapositive of the inverse of the statement:

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


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)


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×