Advertisements
Advertisements
Question
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If demand falls, then price does not increase.
Advertisements
Solution
Let p : demand falls.
q : Price does not increase.
The given statement is p → q.
But p → q ≡ ~ p ∨ q.
∴ The given statement can be written as ‘Demand does not fall or price does not increase’.
Notes
The answer in the textbook is incorrect.
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 the truth table, prove the following logical equivalence :
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.
x is not irrational number but is a square of an integer.
Construct the truth table of the following statement pattern.
[(p → q) ∧ q] → p
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 → p)
Construct the truth table of the following:
[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∧ q) is T
Express the following statement in symbolic form.
Milk is white or grass is green.
Write the truth value of the negation of the following statement.
`sqrt5` is an irrational number.
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.
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 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.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Mona likes Mathematics and Physics.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If a real number is not rational, then it must be irrational.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
Proof is lengthy and it is not interesting.
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
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 it rains then the principal declares a holiday.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Write the following statements in symbolic form
If Kutab – Minar is in Delhi then Taj - Mahal is in Agra
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively
If p, q are true statement and r is false statement, then which of the following statements is a true statement.
Let p, q and r be any three logical statements. Which of the following is true?
Express the following compound statement symbolically:
Delhi is in India but Dhaka is not in Sri Lanka
