Advertisements
Advertisements
प्रश्न
Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."
Advertisements
उत्तर
Let p: 2 + 5 = 10;
q: 4 + 10 = 20
Converse: q → p
If 4 + 10 = 20
Then 2 + 5 = 10
Inverse: ∼ p → ∼ q
lf 2 + 5 ≠ 10
Then 4 + 10 ≠ 20
Contrapositive: ∼ q →∼ p
lf 4 + 10 ≠ 20
Then 2 + 5 ≠ 10.
APPEARS IN
संबंधित प्रश्न
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.
Angle is neither acute nor obtuse.
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Construct the truth table of the following:
∼ (∼p ∧ ∼q) ∨ q
Write the following statement in symbolic form.
Milk is white if and only if the sky is not blue.
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 → 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]
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 ______.
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.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that Ram is tall and handsome.
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.
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
Stock prices are high or stocks are not rising iff stocks are rising.
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 p → q
Choose the correct alternative:
A biconditional statement is the conjunction of two ______ statements
Negation of “Some men are animal” is ______.
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The inverse of the statement "If its quality is good. then it is expensive.", is ______
The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) is equivalent to ______
Write the negation of (p `leftrightarrow` q).
Using truth table prove that:
~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)
