Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let p : D is dog.
q : D is very good.
Then the given statement in the symbolic form is
- p → q
- q → p
- ~q → ~p
- ~p → ~q
| p | q | ~p | ~q | p → q | q → p | ~q → ~p | ~p → ~q |
| T | T | F | F | T | T | T | T |
| T | F | F | T | F | T | F | T |
| F | T | T | F | T | F | T | F |
| F | F | T | T | T | T | T | T |
Since the entries in (i) and (iii) columns are the same, they have the same meaning.
Also, the entries in (ii) and (iv) columns are the same. they have the same meaning.
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.
x is not irrational number but is a square of an integer.
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 → r)] → (p → r)
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra
Write the truth value of the negation of the following statement.
`sqrt5` is an irrational number.
Write the truth value of the negation of the following statement.
London is in England.
Write the following statement in symbolic form.
If triangle is equilateral then it is equiangular.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
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.
Find the truth value of the following statement.
3 is a prime number and an odd number.
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.
If Sunday is not holiday then Ram studies on holiday.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
Kavita is brilliant and brave.
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.
x3 + y3 = (x + y)3 if xy = 0.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is not true that the proof is lengthy but it is interesting.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is interesting iff the proof is lengthy.
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 → 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) ∧ r
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
The inverse of the statement "If its quality is good. then it is expensive.", is ______
Conditional of p → q is equivalent to p → ∼ q.
Which of the following is logically equivalent to `∼(∼p \implies q)`?
Express the following compound statement symbolically:
Delhi is in India but Dhaka is not in Sri Lanka
Write the negation of p ↔ q.
