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Write the following compound statement symbolically. Hima Das wins gold medal if and only if she runs fast. - Mathematics and Statistics

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प्रश्न

Write the following compound statement symbolically. 

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

बेरीज

उत्तर

Let p: Hima Das wins gold medal

Let q: She runs fast.

Then the symbolic form of the given statement is p↔q.

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पाठ 1: Mathematical Logic - Exercise 1.1 [पृष्ठ ७]

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संबंधित प्रश्‍न

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

[~(~p ∧ ~q)] v q


Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


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 converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu.


Write the following compound statement symbolically.

Angle is neither acute nor obtuse.


Write the following compound statement symbolically.

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


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 ∧ r)]


Construct the truth table of the following statement pattern.

(∼ p → ∼ q) ∧ (∼ q → ∼ p)


Construct the truth table of the following statement pattern.

(p ∨ ∼ q) → (r ∧ p)


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


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Express the following statement in symbolic form.

Milk is white or grass is green.


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.

It is false that Nagpur is capital of Maharashtra


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 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.

It is not true that 3 − 7i is a real number.


Find the truth value of the following statement.

If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.


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 ∧ (q ∧ r)


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

(p → q) ∨ (r ∧ s) 


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

~ [(~ p ∨ s) ∧ (~ 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]


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.

q → p


Fill in the blanks :

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


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.

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.

The necessary condition for existence of a tangent to the curve of the function is continuity.


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.

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 ∨ q


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 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.

Kanchanganga is in India and Everest is in Nepal.


Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.


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 a quadrilateral is rhombus then it is not a square.


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

If it rains then the principal declares a holiday.


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.


Negation of p → (p ˅ ∼ q) is ______


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


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


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


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)


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 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 ______ 


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? 


Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."


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 ______.


Converse of the statement q `rightarrow` p is ______.


Write the following statement in symbolic form.

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


Write the following statement in symbolic form.

4 is an odd number if 3 is not a prime factor of 6.


Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka


Write the contrapositive of the inverse of the statement:

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


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.

Using the statements

p: Seema is fat,

q: Seema is happy,

Write the following statements in symbolic form;

  1. Seema is thin and happy.
  2. If Seema is fat then she is unhappy.

Write the negation of (p `leftrightarrow` q).


Using truth table prove that:

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


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