Advertisements
Advertisements
प्रश्न
Write down the following statements in symbolic form :
(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls
Advertisements
उत्तर
(a) p ≡ A triangle is equilateral & q ≡ A traingle is equiangular
∴Symbolic form p↔q
(b) Let p ≡ Price increases & q≡Demand falls
∴ Symbolic form p ∧ q
APPEARS IN
संबंधित प्रश्न
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
Evaluate: ∫ x . log x dx
Write the following compound statement symbolically.
Angle is neither acute nor obtuse.
Write the following compound statement symbolically.
If ΔABC is right-angled at B, then m∠A + m∠C = 90°.
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:
(∼p ∨ ∼q) ↔ [∼(p ∧ q)]
Construct the truth table of the following:
∼ (∼p ∧ ∼q) ∨ 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.
Even though it is cloudy, it is still raining.
Write the truth value of the following statement.
The Himalayas are the highest mountains but they are part of India in the North East.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra
Write the negation of the following statement.
2 + 3 ≠ 5
Write the following statement in symbolic form.
If triangle is equilateral then it is equiangular.
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
Write the following statement in symbolic form.
Stock prices are high if and only if stocks are rising.
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)
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]
Fill in the blanks :
Conjunction of two statement p and q is symbolically written as ______.
Negation of “some men are animal” is ______.
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.
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)
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If demand falls, then price does not increase.
Write the negation of the following.
Kanchanganga is in India and Everest is in Nepal.
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.
I will have tea or coffee.
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
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
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
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.
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
