Advertisements
Advertisements
प्रश्न
Using the truth table check whether the statements ¬(p v q) v (¬p ∧ q) and ¬p are logically equivalent
Advertisements
उत्तर
| p | q | ¬p | p v q | ¬(p v q) | ¬p ∧ q | ¬(p v q) v (¬p ∧ q) |
| T | T | F | T | F | F | F |
| T | F | F | T | F | F | F |
| F | T | T | T | F | T | T |
| F | F | T | F | T | F | T |
From the table, it is clear that ¬P
¬(p v q) v (¬p ∧ q) are logically equivalent
i.e. ¬(p v q) v (¬p ∧ q) ≡ ¬p
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
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
Write the following sentences in symbolic form using statement variables p and q.
19 is not a prime number
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?
3n ≤ 81, n ∈ N
Which one of the following sentences is a proposition?
Peacock is our national bird
Write the converse, inverse, and contrapositive of the following implication.
If a quadrilateral is a square then it is a rectangle
Construct the truth table for the following statement.
¬P ∧ ¬q
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 → q) ↔ (¬p → q)
Prove p → (q → r) ≡ (p ∧ q) → r without using the truth table
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:
| p | q | (p ∧ q) → ¬p |
| T | T | (a) |
| T | F | (b) |
| F | T | (c) |
| F | F | (d) |
Which one of the following is correct for the truth value of (p ∧ q) → ¬p
Choose the correct alternative:
Determine the truth value of each of the following statements:
(a) 4 + 2 = 5 and 6 + 3 = 9
(b) 3 + 2 = 5 and 6 + 1 = 7
(c) 4 + 5 = 9 and 1 + 2 = 4
(d) 3 + 2 = 5 and 4 + 7 = 11
