Advertisements
Advertisements
प्रश्न
Prove that q → p ≡ ¬p → ¬q
Advertisements
उत्तर
| p | q | q → p | ¬p | ¬q | ¬p → ¬q |
| T | T | T | F | F | T |
| T | F | T | F | T | T |
| F | T | F | T | F | F |
| F | F | T | T | T | T |
The entries in the columns corresponding to q → p and ¬p → ¬q are identical and hence they are equivalent.
∴ q → q = ¬p → ¬q
Hence proved.
APPEARS IN
संबंधित प्रश्न
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
P ∧ ¬q
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
¬p v q
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
p → ¬q
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
p ↔ q
Write the following sentences in symbolic form using statement variables p and q.
19 is a prime number or all the angles of a triangle are not equal
Write the following sentences in symbolic form using statement variables p and q.
19 is a prime number and all the angles of a triangle are equal
Determine the truth value of the following statement.
If 6 + 2 = 5, then the milk is white.
Determine the truth value of the following statement.
It is not true that 5 + 5 = 9 or Earth is a planet
Which one of the following sentences is a proposition?
4 + 7 = 12
Which one of the following sentences is a proposition?
What are you doing?
Which one of the following sentences is a proposition?
Peacock is our national bird
Construct the truth table for the following statement
(¬p → r) ∧ (p ↔ q)
Verify whether the following compound propositions are tautologies or contradictions or contingency.
(p ∧ q) ∧¬ (p v q)
Verify whether the following compound propositions are tautologies or contradictions or contingency.
((p v q) ∧¬p) → q
Show that ¬(p ↔ q) ≡ p ↔ ¬q
Check whether the statement p → (q → p) is a tautology or a contradiction without using the truth table
Choose the correct alternative:
If a compound statement involves 3 simple statements, then the number of rows in the truth table is
Choose the correct alternative:
Which one is the contrapositive of the statement (p v q) → r?
Choose the correct alternative:
In the last column of the truth table for ¬(p v ¬q) the number of final outcomes of the truth value ‘F’ is
Choose the correct alternative:
Which one of the following is not true?
