Advertisements
Advertisements
प्रश्न
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.
उत्तर
The given statement can also be expressed as ‘If the function is continuous, then the tangent to the curve exists’.
Let p : The function is continuous
q : The tangent to the curve exists.
∴ p → q is the symbolic form of the given statement.
Notes
The answer in the textbook is incorrect.
APPEARS IN
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
Evaluate: ∫ x . log x dx
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) ↔ (q ∨ r)
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
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.
Earth is a planet and Moon is a star.
Write the truth value of the negation of the following statement.
London is in England.
Write the following statement in symbolic form.
Stock prices are high if and only if stocks are rising.
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 → q) ↔ ~(p ∨ 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.
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
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.
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
Write the negation of the following.
Kanchanganga is in India and Everest is in Nepal.
A biconditional statement is the conjunction of two ______ statements.
If p → q is an implication, then the implication ∼ q → ∼ p is called its
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
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
If q: There are clouds in the sky then p: it is raining. The symbolic form is ______
Which of the following is false?
The inverse of the statement "If its quality is good. then it is expensive.", is ______
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 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."
From the following set of statements, select two statements which have similar meaning.
- If a man is judge, then he is honest.
- If a man is not a judge, then he is not honest.
- If a man is honest, then he is a judge.
- 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)
