Advertisements
Advertisements
Question
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If price increases, then demand falls.
Advertisements
Solution
Let p : Prince increases.
q : demand falls.
The given statement is p → q.
But p → q ≡ ~p ∨ q.
The given statement can be written as ‘Price does not increase or demand falls’.
Notes
The answer in the textbook is incorrect.
APPEARS IN
RELATED QUESTIONS
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
Write the following compound statement symbolically.
Hima Das wins gold medal if and only if she runs fast.
Construct the truth table of the following statement pattern.
[p → (q → r)] ↔ [(p ∧ q) → r]
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∨ q) → q is F
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
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.
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) ∨ (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) → r] ∨ ~ [~ (p → q) ∨ s]
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.
The necessary condition for existence of a tangent to the curve of the function is continuity.
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.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is not true that the proof is lengthy but it is interesting.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is interesting iff the proof is lengthy.
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 x ∈ A ∩ B, then x ∈ A and x ∈ B.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
Stock prices are high or stocks are not rising iff stocks are rising.
Write the negation of the following statement.
10 > 5 and 3 < 8
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Find the negation of 10 + 20 = 30
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
The negation of (p ∨ ∼q) ∧ q is ______
Let p, q and r be any three logical statements. Which of the following is true?
Which of the following is logically equivalent to `∼(∼p \implies q)`?
From the following set of statements, select two statements which have similar meaning.
- If a man is judge, then he is honest.
- If a man is not a judge, then he is not honest.
- If a man is honest, then he is a judge.
- If a man is not honest, then he is not a judge.
