English

Write the Negation of the Following Statement : If the Lines Are Parallel Then Their Slopes Are Equal. - Mathematics and Statistics

Advertisements
Advertisements

Question

Write the negation of the following statement : 
If the lines are parallel then their slopes are equal.

Sum
Advertisements

Solution

The lines are parallel and their - slopes are not equal.

shaalaa.com
  Is there an error in this question or solution?
2015-2016 (March)

APPEARS IN

RELATED QUESTIONS

Write the dual of the following statements: (p ∨ q) ∧ T


Using the truth table prove the following logical equivalence.

∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p


Using the truth table prove the following logical equivalence.

p → (q ∧ r) ≡ (p → q) ∧ (p → r)


Using the truth table, prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

(p ↔ q) ∧ (p → ∼ q)


Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

(∼ p → q) ∧ (p ∧ r)


Prove that the following statement pattern is a tautology.

(p ∧ q) → q


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


Prove that the following statement pattern is a contradiction.

(p → q) ∧ (p ∧ ~ q)


Using the truth table, verify.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Write the dual statement of the following compound statement.

A number is a real number and the square of the number is non-negative.


Using the rules of negation, write the negation of the following:

(p → r) ∧ q


Determine whether the following statement pattern is a tautology, contradiction, or contingency.

[(~p ∧ q) ∧ (q ∧ r)] ∨ (~q)


Determine whether the following statement pattern is a tautology, contradiction, or contingency.

[p → (~q ∨ r)] ↔ ~[p → (q → r)]


The equivalent form of the statement ~(p → ~ q) is ______.


The converse of contrapositive of ∼p → q is ______.


Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×