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
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
Construct the truth table of the following statement pattern.
(p ∧ q) ↔ (q ∨ r)
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Write the negation of the following statement.
2 + 3 ≠ 5
Write the following statement in symbolic form.
If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.
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
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.
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.
The drug is effective though it has side effects.
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.
Write the negation of the following.
Ramesh is intelligent and he is hard working.
Negation of p → (p ˅ ∼ q) is ______
Write the following statements in symbolic form
Even though it is not cloudy, it is still raining
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
Write the negation of p → q
If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______
If p and q are true and rands are false statements, then which of the following is true?
Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
The negation of ∼s ∨ (∼r ∧ s) is equivalent to ______
The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' 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 ______.
Converse of the statement q `rightarrow` p is ______.
Write the following statement in symbolic form.
4 is an odd number if 3 is not a prime factor of 6.
Write the contrapositive of the inverse of the statement:
‘If two numbers are not equal, then their squares are not equal’.
