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प्रश्न
Write the following statement in symbolic form:
Milk is white if and only if the sky is not blue.
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उत्तर
Let p: Milk is white.
q: Sky is blue.
The given statement in symbolic form is p ↔ ∼q.
संबंधित प्रश्न
Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).
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
Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
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.
Hima Das wins gold medal if and only if she runs fast.
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) ↔ (q ∨ r)
Construct the truth table of the following statement pattern.
p → [∼ (q ∧ r)]
Construct the truth table of the following statement pattern.
(q → p) ∨ (∼ 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) → q is F
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
Express the following statement in symbolic form.
e is a vowel or 2 + 3 = 5
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 truth value of the negation of the following statement.
`sqrt5` is an irrational number.
Find the truth value of the following statement.
If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.
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)]
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)
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is not holiday or Ram studies on holiday.
Assuming that the following statement is true,
p : Sunday is holiday,
q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is a holiday and Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement:
p ↔ ~ q
Negation of “some men are animal” is ______.
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.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
If proof is lengthy then it is 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
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
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.
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.
A biconditional statement is the conjunction of two ______ statements.
If p → q is an implication, then the implication ∼ q → ∼ p is called its
Find the negation of 10 + 20 = 30
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
Which of the following is NOT true for p → q.
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."
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
Express the following compound statement symbolically:
3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25
If p, q are true statements and r, s are false statements, then write the truth value of the compound statement
(p `→` ∼ r) `→` (q ∧ s)
