English

Choose the correct alternative: If p is any statement, then (p ˅ ~p) is a - Mathematics and Statistics

Advertisements
Advertisements

Question

Choose the correct alternative:

If p is any statement, then (p ˅ ~p) is a

Options

  • Contingency

  • Contradiction

  • Tautology

  • None of these

MCQ

Solution

Tautology

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.1: Mathematical Logic - Q.1

RELATED QUESTIONS

Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "


Using truth table examine whether the following statement pattern is tautology, contradiction or contingency `(p^^~q) harr (p->q)`


Show that the following statement pattern in contingency : 

(~p v q) → [p ∧ (q v ~ q)] 


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


Examine whether the following statement (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.


Using the truth table prove the following logical equivalence.

p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]


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.

∼ (∼ q ∧ p) ∧ q


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

[p → (∼ q ∨ r)] ↔ ∼ [p → (q → 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 → (q → r)] ↔ [(p ∧ q) → r]


Prepare truth tables for the following statement pattern.

(p ∧ r) → (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


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ (~p ∨ ~q)


Show that the following statement pattern is contingency.

p ∧ [(p → ~ q) → q]


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Write the dual of the following:

(p ∨ q) ∨ r


Write the dual of the following:

p ∨ (q ∨ r) ≡ (p ∨ q) ∨ r


Write the dual statement of the following compound statement.

13 is prime number and India is a democratic country.


Write the dual statement of the following compound statement.

Radha and Sushmita cannot read Urdu.


Write the dual statement of the following compound statement.

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


Write the negation of the following statement.

All the stars are shining if it is night.


With proper justification, state the negation of the following.

(p → q) ∧ r


Construct the truth table for the following statement pattern.

(p ∧ ~ q) ↔ (q → p)


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) ∧ ~(q ∧ ~p)


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

If a man is bachelor, then he is happy.


Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


Which of the following is not equivalent to p → q.


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


Write the negation of the following statement:

(p `rightarrow` q) ∨ (p `rightarrow` r)


Show that the following statement pattern is a contingency:

(p→q)∧(p→r)


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×