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
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.
[~(~p ∧ ~q)] v q
Evaluate: ∫ x . log x dx
Write the following compound statement symbolically.
Nagpur is in Maharashtra and Chennai is in Tamil Nadu.
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.
(q → p) ∨ (∼ p ↔ q)
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 truth value of the following statement.
The Himalayas are the highest mountains but they are part of India in the North East.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra
Write the following statement in symbolic form.
It is not true that “i” is a real number.
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.
Kavita is brilliant and brave.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The necessary condition for existence of a tangent to the curve of the function is continuity.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
It is not true that intelligent persons are neither polite nor helpful.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If the question paper is not easy then we shall not pass.
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.
Ramesh is intelligent and he is hard working.
Find the negation of 10 + 20 = 30
Without using truth table prove that:
~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
Write the negation of p → q
Choose the correct alternative:
Negation of p → (p ˅ ~q) is
State whether the following statement is True or False:
The converse of inverse of ~ p → q is q → ~ p
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
The negation of (p ∨ ∼q) ∧ q is ______
If p : A man is happy, q : A man is rich, then the symbolic form of ‘A man is neither happy nor rich is ______.
Write the following statement in symbolic form.
It is not true that `sqrt(2)` is a rational number.
