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Construct the truth table of the following: [(∼p ∨ q) ∧ (q → r)] → (p → r)

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प्रश्न

Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)

योग
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उत्तर

p q r ∼p ∼p ∨ q q→r (∼p∨q) ∧ (q→r) p→r [(∼p∨q) ∧ (q→r)] → (p→r)
T T T F T T T T T
T T F F T F F F T
T F T F F T F T T
T F F F F T F F T
F T T T T T T T T
F T F T T F F T T
F F T T T T T T T
F F F T T T T T T
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अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

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बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 6.5 | पृष्ठ ३३

वीडियो ट्यूटोरियलVIEW ALL [3]

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 the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


Write the following compound statement symbolically. 

Hima Das wins gold medal if and only if she runs fast.


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.

(q → p) ∨ (∼ p ↔ q)


Construct the truth table of the following statement pattern.

(p ∨ ∼ q) → (r ∧ p)


Construct the truth table of the following:

p → (q → p)


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 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 following statement in symbolic form.

If triangle is equilateral then it is equiangular.


Write the following statement in symbolic form.

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


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.

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) ↔ ~(p ∨ q)


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.


Fill in the blanks :

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


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.

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


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 price increases, then demand falls.


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


Write the following statements in symbolic form

Even though it is not cloudy, it is still raining


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Negation of p → (p ˅ ~q) is


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


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


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


The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______


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


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The statement ∼(p ↔ ∼q) is ______.


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Write the negation of p ↔ q.


Using truth table prove that:

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


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