Advertisements
Advertisements
Question
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.
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate: ∫ x . log x dx
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 ∧ r)]
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
Construct the truth table of the following statement pattern.
(p ∨ ∼ q) → (r ∧ p)
Construct the truth table of the following:
∼ (∼p ∧ ∼q) ∨ q
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 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.
London is in England.
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.
Neither 27 is a prime number nor divisible by 4.
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.
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.
3 is prime number if 3 is perfect square number.
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.
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.
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.
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
If p and q are true and rands are false statements, then which of the following is true?
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?
Which of the following is logically equivalent to `∼(∼p \implies q)`?
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
