English

The negation of the statement (p ˄ q) → (r ˅ ∼ p) is ______.

Advertisements
Advertisements

Question

The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.

Options

  • p ˄ q ˄ ∼ r

  • (p ˄ q) ˅ r

  • p ˅ q ˅ ∼ r

  • (p v q) ˄ (r ˅ s)

MCQ
Fill in the Blanks
Advertisements

Solution

The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is p ˄ q ˄ ∼ r.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.1: Mathematical Logic - MCQ

RELATED QUESTIONS

Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).


Write the following compound statement symbolically.

The angle is right angle if and only if it is of measure 90°.


Write the following compound statement symbolically.

If ΔABC 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) ↔ (p → q)


Construct the truth table of the following statement pattern.

(∼ p → ∼ q) ∧ (∼ q → ∼ p)


Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


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


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.

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 ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ 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.

Sunday is not holiday or Ram studies on holiday.


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q ∧ ~ p


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.

The Sun has set and Moon has risen.


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.


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.

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.

If the question paper is not easy then we shall not pass.


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 ∨ 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) ∧ r


Write the negation of the following.

If ∆ABC is not equilateral, then it is not equiangular.


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.


Write the negation of the following statement.

I will have tea or coffee.


Find the negation of 10 + 20 = 30


Without using truth table show that -

(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)


State whether the following statement is True or False:

The converse of inverse of ~ p → q is q → ~ p


Negation of “Some men are animal” is ______.


Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra


If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.


If p, q are true statement and r is false statement, then which of the following statements is a true statement.


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


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


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 ______.


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


Write the contrapositive of the inverse of the statement:

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


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)


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.

Using truth table prove that:

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×