हिंदी

Using Truth Table, Examine Whether the Following Statement Pattern is Tautology, Contradiction Or Contingency: P ∨ ∼(P ∧ Q) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Using truth table, examine whether the following statement pattern is tautology, contradiction or contingency: p ∨ [∼(p ∧ q)]

योग

उत्तर

Truth Table

(1) (2) (3) (4) (5)
p q p ∧ q ∼(p ∧ q) p ∨ [∼(p ∧ q)]
T T T F T
T F F T T
F T F T T
F F F T T

All entries in coloumn (5) are T's

p ∨ [∼(p ∧ q)] is Tautology.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2016-2017 (July) Set 1

APPEARS IN

संबंधित प्रश्न

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

[(p→q) ∧ q]→p


Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)


Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."


Use the quantifiers to convert the following open sentence defined on N into true statement
5x - 3 < 10


Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)


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 ∧ 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.

∼ (∼ q ∧ p) ∧ q


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

(p ∧ ∼ q) ↔ (p → q)


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

(p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)


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

[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r


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

(p → q) ∨ (q → p)


Prepare truth tables for the following statement pattern.

p → (~ p ∨ q)


Prepare truth table for (p ˄ q) ˅ ~ r

(p ∧ q) ∨ ~ r


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 pair of statement pattern is equivalent.

p ↔ q and (p → q) ∧ (q → p)


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.

Karina is very good or everybody likes her.


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.

Some continuous functions are differentiable.


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

(~p ∧ q) ∧ (~q ∨ ~r)


With proper justification, state the negation of the following.

(p → q) ∨ (p → r)


Construct the truth table for the following statement pattern.

(p ∨ r) → ~(q ∧ r)


What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.


Using the truth table, prove the following logical equivalence.

p ∧ (~p ∨ q) ≡ p ∧ q


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

2 is even number or 9 is a perfect square.


Examine whether the statement pattern

[p → (~ q ˅ r)] ↔ ~[p → (q → r)] is a tautology, contradiction or contingency.


Complete the truth table.

p q r q → r r → p (q → r) ˅ (r → p)
T T T T `square` T
T T F F `square` `square`
T F T T `square` T
T F F T `square` `square`
F T T `square` F T
F T F `square` T `square`
F F T `square` F T
F F F `square` T `square`

The given statement pattern is a `square`


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


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)


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

(∼p ∧ ∼q) → (p → q)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×