Advertisements
Advertisements
Question
Write the negation of the following.
Quadrilateral is a square if and only if it is a rhombus.
Advertisements
Solution
Let p: Quadrilateral is a square.
q: It is a rhombus.
Then the symbolic form of the given statement is p↔q.
Since ∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p), the negation of the given statement is:
Quadrilateral is a square but it is not a rhombus or quadrilateral is a rhombus but it is not a square.
APPEARS IN
RELATED QUESTIONS
Write the negation of the following.
`sqrt2` is a rational number.
Write the negation of the following.
Polygon ABCDE is a pentagon.
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.
It is cold and raining.
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
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 → (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:
∃ x ∈ A, such that x + 9 ≤ 15.
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 ______.
Negation of (p ∧ q) → (∼p ∨ r) 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 ______.
