English

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. - Mathematics and Statistics

Advertisements
Advertisements

Question

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.

Sum
Advertisements

Solution

Symbolic form of the given statement is
~ p → ~ q

∴ ~ p → ~ q ≡ ~ T → ~ T

≡ F → F

≡ T

Hence, truth value is T.

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

APPEARS IN

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.


Write the following compound statement symbolically.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Construct the truth table of the following:

[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


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 following statement.

A quadratic equation has two distinct roots or 6 has three prime factors.


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 truth value of the negation of the following statement.

`sqrt5` is an irrational 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) ↔ ~(p ∨ q)


Assuming the first statement p and second as q. Write the following statement in symbolic form.

Even though it is not cloudy, it is still raining.


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


Consider the following statements.

  1. If D is dog, then D is very good.
  2. If D is very good, then D is dog.
  3. If D is not very good, then D is not a dog.
  4. If D is not a dog, then D is not very good. 

Identify the pairs of statements having the same meaning. Justify.


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


Write the following statement in symbolic form:

Milk is white if and only if the sky is not blue.


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)


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


Negation of “Some men are animal” is ______.


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


The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______


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


Express the following compound statement symbolically:

Delhi is in India but Dhaka is not in Sri Lanka


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×