Advertisements
Advertisements
Question
Write the following statement in symbolic form.
Stock prices are high if and only if stocks are rising.
Advertisements
Solution
Let p : Stock prices are high.
q : Stock are rising
The symbolic form is p ↔ q.
APPEARS IN
RELATED QUESTIONS
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
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.
x is not irrational number but is a square of an integer.
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∧ q) is T
Find the truth value of the following statement.
Neither 27 is a prime number nor divisible by 4.
Find the truth value of the following statement.
3 is a prime number and an odd number.
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 ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
Negation of “some men are animal” is ______.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that intelligent persons are neither polite nor helpful.
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 price increases, then demand falls.
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Write the negation of the following.
If x ∈ A ∩ B, then x ∈ A and x ∈ B.
Write the negation of the following statement.
10 > 5 and 3 < 8
If p → q is an implication, then the implication ∼ q → ∼ p is called its
Write the following statements in symbolic form
If Kutab – Minar is in Delhi then Taj - Mahal is in Agra
Choose the correct alternative:
A biconditional statement is the conjunction of two ______ statements
Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)

The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
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?
Which of the following is logically equivalent to `∼(∼p \implies q)`?
The statement ∼(p ↔ ∼q) is ______.
Write the negation of (p `leftrightarrow` q).
