हिंदी

Show that the following statement pattern is contingency. (p ∧ ~q) → (~ p ∧ ~ q) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Show that the following statement pattern is contingency.

(p∧~q) → (~p∧~q)

योग
Advertisements

उत्तर

p q ~p ~q p∧~q ~p∧~q (p∧~q)→(~p∧~q)
T T F F F F T
T F F T T F F
F T T F F F T
F F T T F T T

The truth values in the last column are not identical. Hence, it is contingency.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Exercise 1.6 [पृष्ठ १६]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.6 | Q 5.1 | पृष्ठ १६

संबंधित प्रश्न

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

[(p→q) ∧ q]→p


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


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 the negation of the Following Statement :
∀ y ∈  N, y2 + 3 ≤ 7


By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency.  (p →  q) ∧  (p ∧ ~ q ).


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 → r) ∧ (q → r)


Using the truth table proves the following logical equivalence.

∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)


Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .


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

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


Prepare truth tables for the following statement pattern.

p → (~ 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.

(p ∧ ~ q) → (~ p ∧ ~ q)


Prove that the following statement pattern is a tautology.

(~ p ∨ ~ q) ↔ ~ (p ∧ q)


Show that the following statement pattern is contingency.

(p → q) ↔ (~ 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.


Write the negation of the following statement.

∀ n ∈ N, n + 1 > 0


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

"If it snows, then they do not drive the car"


With proper justification, state the negation of the following.

(p → q) ∨ (p → r)


Construct the truth table for the following statement pattern.

(p ∧ r) → (p ∨ ~q)


Construct the truth table for the following statement pattern.

(p ∨ r) → ~(q ∧ r)


Construct the truth table for the following statement pattern.

(p ∨ ~q) → (r ∧ p)


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

[p → (~q ∨ r)] ↔ ~[p → (q → r)]


Write the dual of the following.

(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)


Choose the correct alternative:

If p → q is an implication, then the implication ~q → ~p is called its


Write the dual of the following.

13 is prime number and India is a democratic country


Examine whether the statement pattern

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


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×