Advertisements
Advertisements
Question
Using the truth table check whether the statements ¬(p v q) v (¬p ∧ q) and ¬p are logically equivalent
Advertisements
Solution
| 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
RELATED QUESTIONS
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 not a prime number
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?
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
Verify whether the following compound propositions are tautologies or contradictions or contingency.
((p v q) ∧¬p) → q
Show that ¬(p → q) ≡ p ∧¬q
Show that p → q and q → p are not equivalent
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:
Which one of the following statements has truth value F?
Choose the correct alternative:
Which one is the contrapositive of the statement (p v q) → r?
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:
Which one of the following is not true?
