Advertisements
Advertisements
Question
Using the rule of negation write the negation of the following with justification.
p → (p ∨ ∼ q)
Solution
The negation of p → (p ∨ ∼ q) is ∼ [p → (p ∨ ∼ q)] ≡ p ∧ ∼ (p ∨ ∼ q) .......(Negation of implication)
≡ p ∧ [∼ p ∧ ∼ (∼ q)] .....(Negation of disjunction)
≡ p ∧ (∼ p ∧ q) .......(Negation of negation)
RELATED QUESTIONS
Write the negation of the following.
3 is not a root of the equation x2 + 3x – 18 = 0
Write the negation of the following.
`sqrt2` is a rational number.
Write the negation of the following.
Write the negation of the following.
x + 8 > 11 or y – 3 = 6
Write the negation of the following.
11 < 15 and 25 > 20
Write the negation of the following.
Quadrilateral is a square if and only if it is a rhombus.
Write the negation of the following.
If it is raining then we will go and play football.
Write the negation of the following.
All-natural numbers are whole numbers.
Write the negation of the following.
∀ n ∈ N, n2 + n + 2 is divisible by 4.
Write the negation of the following.
∃ x ∈ N such that x – 17 < 20
Using the rule of negation write the negation of the following with justification.
∼ q → p
Using the rule of negation write the negation of the following with justification.
p ∧ ∼ q
Using the rule of negation write the negation of the following with justification.
(p ∨ ∼ q) ∧ r
Using the rule of negation write the negation of the following with justification.
∼ (p ∧ q) ∨ (p ∨ ∼ q)
Using the rule of negation write the negation of the following with justification.
(p ∨ ∼ q) → (p ∧ ∼ q)
Using the rule of negation write the negation of the following with justification.
(∼ p ∨ ∼ q) ∨ (p ∧ ∼ q)
Select and write the correct answer from the given alternative of the following question:
The negation of inverse of ∼p → q is ________.
The negation of p ∧ (q → r) is ________.
Write the negation of the following:
∀ n ∈ A, n + 7 > 6.
Write the negation of the following:
Some triangles are equilateral triangle.
The negation of the statement 'He is poor but happy' is ______.
The negation of the statement pattern ~ p v(q → ~ r) is ______.
Negation of the statement 'A is rich but silly' is ______
Negation of (∼p → q) is ______.
The negation of the statement, ∃ x ∈ R, such that x3 + 8 > 0, is ______.
The negation of p ^ (q → r) is ______.
The negation of the statement 7 is greater than 4 or 6 is less than 7.
The negation of (p → q) ∧ r is ______.
