English

Write the negation of the following statement. I will have tea or coffee.

Advertisements
Advertisements

Question

Write the negation of the following statement.

I will have tea or coffee.

Sum
Advertisements

Solution

Let p : I will have tea.
q : I will have coffee.

The given statement in symbolic form is p ∨ q.

Its negation is ~(p ∨ q) ≡ ~p ∧ ~q.

∴ The negation of given statement is ‘I will not have tea and coffee’.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 34]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.22 | Page 34

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

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 that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p


Evaluate: ∫ x . log x dx


Construct the truth table of the following statement pattern.

(∼ p → ∼ q) ∧ (∼ q → ∼ p)


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


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.

16 is an even number and 8 is a perfect square.


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.


Find the truth value of the following statement.

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


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)


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 ______.


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.

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.

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.

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


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If price increases, then demand falls.


Write the negation of the following.

Ramesh is intelligent and he is hard working.


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 ______ 


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


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.


If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.


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)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×