English

With proper justification, state the negation of the following. (p → q) ∧ r - Mathematics and Statistics

Advertisements
Advertisements

Question

With proper justification, state the negation of the following.

(p → q) ∧ r

Sum

Solution

~[(p → q) ∧ r]

≡ ~ (p → q) ∨ ~ r    ....[Negation of conjunction]

≡ (p ∧ ~q) ∨ ~ r      ....[Negation of implication]

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Exercise 1.8 [Page 21]

APPEARS IN

RELATED QUESTIONS

Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”


Write the dual of the following statements:

Madhuri has curly hair and brown eyes.


Write converse and inverse of the following statement: 
“If a man is a bachelor then he is unhappy.” 


If   p : It is raining
     q : It is humid

Write the following statements in symbolic form:

(a) It is raining or humid.
(b) If it is raining then it is humid.
(c) It is raining but not humid. 


Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."


Using the truth table prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


Using the truth table proves the following logical equivalence.

∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)


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)


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

[(p ∨ q) ∧ ∼p] ∧ ∼q


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

[(p ∧ (p → q)] → q


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

[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r


Prepare truth tables for the following statement pattern.

(~ p ∨ q) ∧ (~ p ∨ ~ q)


Prepare truth tables for the following statement pattern.

(p ∧ r) → (p ∨ ~ q)


Prepare truth table for (p ˄ q) ˅ ~ r

(p ∧ q) ∨ ~ r


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

(~ q ∧ p) ∧ (p ∧ ~ p)


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

~ p → (p → ~ q)


Prove that the following statement pattern is a tautology.

(~p ∧ ~q ) → (p → q)


Prove that the following statement pattern is a tautology.

(~ p ∨ ~ q) ↔ ~ (p ∧ q)


Prove that the following statement pattern is a contradiction.

(p ∨ q) ∧ (~p ∧ ~q)


Prove that the following statement pattern is a contradiction.

(p → q) ∧ (p ∧ ~ q)


Using the truth table, verify

~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q


Using the truth table, verify

~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the dual of the following:

~(p ∧ q) ≡ ~ p ∨ ~ q


Write the dual statement of the following compound statement.

Karina is very good or everybody likes her.


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

(p → r) ∧ q


Construct the truth table for the following statement pattern.

(p ∨ r) → ~(q ∧ r)


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

[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ q)]


Using the truth table, prove the following logical equivalence.

[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


Write the converse, inverse, contrapositive of the following statement.

If a man is bachelor, then he is happy.


State the dual of the following statement by applying the principle of duality.

(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)


Express the truth of the following statement by the Venn diagram.

Some members of the present Indian cricket are not committed.


If p → (∼p v q) is false, then the truth values of p and q are respectively


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


Show that the following statement pattern is a contingency:

(p→q)∧(p→r)


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

(p ∧ q) → (q ∨ p)


If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×