Advertisements
Advertisements
Question
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
Solution
Let p : x3 + y3 = (x + y)3
q : xy = 0
∴ p ↔ q is the symbolic form of the given statement.
APPEARS IN
RELATED QUESTIONS
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
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 → r)] ↔ [(p ∧ q) → r]
Construct the truth table of the following:
[(∼p ∨ q) ∧ (q → r)] → (p → r)
Express the following statement in symbolic form.
Mango is a fruit but potato is a vegetable.
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
Write the truth value of the following statement.
16 is an even number and 8 is a perfect square.
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
Write the truth value of the following statement.
The Himalayas are the highest mountains but they are part of India in the North East.
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 : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q ∧ ~ p
Fill in the blanks :
Conjunction of two statement p and q is symbolically written as ______.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The Sun has set and Moon has risen.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
3 is prime number if 3 is perfect square number.
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) ∧ r
Write the negation of the following.
Kanchanganga is in India and Everest is in Nepal.
Write the negation of the following statement.
10 > 5 and 3 < 8
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
Which of the following is NOT true for p → q.
The statement, 'If I go to school, then I will get knowledge' is equivalent to ______
Let S be a non-empty subset of R. Consider the following statement:
p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p?
Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."
Let p, q and r be any three logical statements. Which of the following is true?
The statement ∼(p ↔ ∼q) is ______.
Let p: I am brave.
q: I will climb the Mount Everest.
The symbolic form of a statement,
‘I am neither brave nor I will climb the mount Everest’ is
