Advertisements
Advertisements
प्रश्न
Express the following statement in symbolic form.
Even though it is cloudy, it is still raining.
उत्तर
Let p : It is cloudy.
q : It is still raining.
The symbolic form is p ∧ q.
APPEARS IN
संबंधित प्रश्न
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p
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 Δ ABC 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.
Construct the truth table of the following statement pattern.
[(p → q) ∧ q] → p
Construct the truth table of the following statement pattern.
∼ p ∧ [(p ∨ ∼ q) ∧ q]
Construct the truth table of the following statement pattern.
(∼ p → ∼ q) ∧ (∼ q → ∼ p)
Construct the truth table of the following:
p → (q → p)
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) is T
Write the truth value of the following statement.
The Himalayas are the highest mountains but they are part of India in the North East.
Write the following statement in symbolic form.
It is not true that “i” is a real number.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
If p and q are true and r and s are false, find the truth value of the following compound statement.
p ∧ (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) ∨ (r ∧ s)
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)
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]
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.
q → p
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If Kiran drives the car, then Sameer will walk.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
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.
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 statement “An angle is a right angle if and only if it is of measure 90°”
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
If q: There are clouds in the sky then p: it is raining. The symbolic form 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 ______
The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______
Let p, q and r be any three logical statements. Which of the following is true?
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.
