Advertisements
Advertisements
प्रश्न
A biconditional statement is the conjunction of two ______ statements.
विकल्प
Negative
Compound
Connective
Conditional
Advertisements
उत्तर
A biconditional statement is the conjunction of two conditional statements.
Explanation:
A biconditional statement (p ⇔ q) means that p is true if and only if q is true. This is equivalent to the conjunction of two conditional statements: p ⇒ q and q ⇒ p. Both conditions must hold true for the biconditional to be true.
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)
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
Evaluate: ∫ x . log x dx
Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.
Write the following compound statement symbolically.
The angle is right angle if and only if it is of measure 90°.
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.
Write the following compound statement symbolically.
x is not irrational number but is a square of an integer.
Construct the truth table of the following statement pattern.
(p ∧ q) ↔ (q ∨ r)
Construct the truth table of the following statement pattern.
[p → (q → r)] ↔ [(p ∧ q) → r]
Construct the truth table of the following statement pattern.
(p ∨ ∼ q) → (r ∧ p)
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∨ q) → q is F
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
Express the following statement in symbolic form.
Even though it is cloudy, it is still raining.
Write the negation of the following statement.
− 3 is a natural number.
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
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.
Find the truth value of the following statement.
Neither 27 is a prime number nor divisible by 4.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement:
p ↔ ~ q
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
~ (p ∨ q)
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The drug is effective though it has side effects.
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
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If demand falls, then price does not increase.
Rewrite the following statement without using the connective ‘If ... then’.
If a quadrilateral is rhombus then it is not a square.
Write the negation of the following statement.
10 > 5 and 3 < 8
Write the negation of the following statement.
∀ n ∈ N, n + 3 > 9.
Negation of p → (p ˅ ∼ q) is ______
The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.
Write the following statement in symbolic form:
Milk is white if and only if the sky is not blue.
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
If p, q are true statement and r is false statement, then which of the following statements is a true statement.
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
Which of the following is false?
If p and q are true and rands are false statements, then which of the following is true?
The negation of (p ∨ ∼q) ∧ q is ______
Which of the following is NOT true for p → q.
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The negation of ∼s ∨ (∼r ∧ s) 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?
The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
Conditional of p → q is equivalent to p → ∼ q.
Converse of the statement q `rightarrow` p is ______.
Express the following compound statement symbolically:
Delhi is in India but Dhaka is not in Sri Lanka
Express the following compound statement symbolically:
3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25
Write the negation of (p `leftrightarrow` q).
