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

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प्रश्न

Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]

तक्ता

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
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पाठ 1: Mathematical Logic - Exercise 1.2 [पृष्ठ १३]

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


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


Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p


Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


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.


Write the following compound statement symbolically.

x is not irrational number but is a square of an integer.


Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (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 statement pattern.

(p ∨ ∼ q) → (r ∧ p)


If p ∧ q is false and p ∨ q is true, then ______ is not true.


Construct the truth table of the following:

(∼p ∨ ∼q) ↔ [∼(p ∧ 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


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.

e is a vowel or 2 + 3 = 5


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 truth value of the following statement.

A quadratic equation has two distinct roots or 6 has three prime factors.


Write the negation of the following statement.

− 3 is a natural number.


Write the negation of the following statement.

It is false that Nagpur is capital of Maharashtra


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.

If triangle is equilateral then it is equiangular.


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.

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.

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


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 ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]


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.

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 –––––––––.


State whether the following statement is True or False:

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.


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

The Sun has set and Moon has risen.


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

Mona likes Mathematics and Physics.


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.

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.
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It is not true that the proof is lengthy but it is interesting.


If p : Proof is lengthy.
q : It is interesting.
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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 → 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


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q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ (p ∨ q) ∧ r


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(Hint : p → q ≡ ∼ p ∨ q)

If demand falls, then price does not increase.


Write the negation of the following.

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


Write the negation of the following.

Kanchanganga is in India and Everest is in Nepal.


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.


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

If 10 − 3 = 7 then 10 × 3 ≠ 30.


Write the negation of the following statement.

I will have tea or coffee.


Negation of p → (p ˅ ∼ q) is ______


A biconditional statement is the conjunction of two ______ statements.


Find the negation of 10 + 20 = 30


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the following statements in symbolic form

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


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°”


Write the following statements in symbolic form.

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


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


If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______ 


Which of the following is false?


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


Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______ 


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


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? 


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


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


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.


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


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