English

If p : He swims q : Water is warm Give the verbal statement for the following symbolic statement: p ↔ ~ q

Advertisements
Advertisements

Question

If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement:

p ↔ ~ q

Very Short Answer
Advertisements

Solution

He swims if and only if water is not warm.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Exercise 1.4 [Page 11]

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


Write the following compound statement symbolically.

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


Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p


Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]


Construct the truth table of the following statement pattern.

(q → p) ∨ (∼ p ↔ q)


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


Construct the truth table of the following:

[(∼p ∨ q) ∧ (q → r)] → (p → r)


Write the negation of the following statement.

All men are animals.


Write the following statement in symbolic form.

It is not true that “i” 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 ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]


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.


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 → r


Write the negation of the following.

Ramesh is intelligent and he is hard working.


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.


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.


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


Without using truth table show that -

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


Negation of “Some men are animal” is ______.


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


Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively


Which of the following is NOT true for p → q.


The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______ 


The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______ 


Conditional of p → q is equivalent to p → ∼ q.


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


Let p: I am brave.
      q: I will climb the Mount Everest.

The symbolic form of a statement,

‘I am neither brave nor I will climb the mount Everest’ is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×