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 → ¬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 and all the angles of a triangle are 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.
China is in Europe dr `sqrt(3)` is art integer
Determine the truth value of the following statement.
11 is a prime number and all the sides of a rectangle are equal
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?
3n ≤ 81, n ∈ N
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 v q) v ¬q
Verify whether the following compound propositions are tautologies or contradictions or contingency.
(p → q) ↔ (¬p → q)
Verify whether the following compound propositions are tautologies or contradictions or contingency.
((p → q) ∧ (q → r)) → (p → r)
Show that ¬(p ↔ q) ≡ p ↔ ¬q
Prove that p → (¬q v r) ≡ ¬p v (¬q v r) using truth table
Choose the correct alternative:
Which one of the following is incorrect? For any two propositions p and q, we have
Choose the correct alternative:
The proposition p∧(¬p∨q)] is
