English

Find the truth value of the following statement. Every accountant is free to apply his own accounting rules if and only if machinery is an asset. - Mathematics and Statistics

Advertisements
Advertisements

Question

Find the truth value of the following statement.

Every accountant is free to apply his own accounting rules if and only if machinery is an asset.

Short Note

Solution

Let p : Every accountant is free to apply his own accounting rules.

q : Machinery is an asset.

The truth values of p and q are F and T respectively.

The given statement in symbolic form is p ↔ q.

∴ p ↔ q ≡ F ↔ T ≡ F

∴ Truth value of the given statement is F.

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

APPEARS IN

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 ∧ ~q).


Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p


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


Construct the truth table of the following statement pattern.

[(p → q) ∧ q] → p


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 ∨ 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) ∧ (∼ q → ∼ p)


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


Construct the truth table of the following:

p → (q → p)


Express the following statement in symbolic form.

Milk is white or grass is green.


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.

2 + 3 ≠ 5


Find the truth value of the following statement.

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


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 → q) ∨ (r ∧ s) 


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 ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

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 ______.


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


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.

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


Rewrite the following statement without using the connective ‘If ... then’.

If a quadrilateral is rhombus then it is not a square.


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


Choose the correct alternative:

Negation of p → (p ˅ ~q) is


State whether the following statement is True or False:

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


Write the following statements in symbolic form.

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


If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.


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


The negation of (p ∨ ∼q) ∧ q is ______


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


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.

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×