Advertisements
Advertisements
प्रश्न
Assuming the first statement p and second as q. Write the following statement in symbolic form.
x3 + y3 = (x + y)3 if xy = 0.
Advertisements
उत्तर
Let p : x3 + y3 = (x + y)3
q : xy = 0
∴ p ↔ q is the symbolic form of the given statement.
APPEARS IN
संबंधित प्रश्न
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Construct the truth table of the following:
∼ (∼p ∧ ∼q) ∨ q
Construct the truth table of the following:
[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]
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 ∨ s) ∧ (~ q ∧ r)]
State whether the following statement is True or False:
The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
To be brave is necessary and sufficient condition to climb the Mount Everest.
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.
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
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Consider the following statements.
- If D is dog, then D is very good.
- If D is very good, then D is dog.
- If D is not very good, then D is not a dog.
- If D is not a dog, then D is not very good.
Identify the pairs of statements having the same meaning. Justify.
Write the negation of the following statement.
7 is prime number and Tajmahal is in Agra.
Write the negation of the following statement.
∃ x ∈ A, such that x + 5 < 11.
A biconditional statement is the conjunction of two ______ statements.
Write the following compound statements symbolically.
Triangle is equilateral or isosceles
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 q: There are clouds in the sky then p: it is raining. The symbolic form is ______
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
The inverse of the statement "If its quality is good. then it is expensive.", is ______
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
Converse of the statement q `rightarrow` p is ______.
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
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.
Using the statements
p: Seema is fat,
q: Seema is happy,
Write the following statements in symbolic form;
- Seema is thin and happy.
- If Seema is fat then she is unhappy.
Construct the truth table for the statement pattern:
[(p → q) ∧ q] → p
