हिंदी

Examine whether the following statement pattern is a tautology, a contradiction or a contingency. (~ q ∧ p) ∧ (p ∧ ~ p) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

(~ q ∧ p) ∧ (p ∧ ~ p)

योग

उत्तर

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

All the truth values in the last column are F. Hence, it is a contradiction.

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] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.6 | Q 2.2 | पृष्ठ १६

संबंधित प्रश्न

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


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


State if the following sentence is a statement. In case of a statement, write down the truth value :
Every quadratic equation has only real roots.


State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.


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


Using the truth table prove the following logical equivalence.

p → (q → p) ≡ ∼ p → (p → q)


Using the truth table prove the following logical equivalence.

(p ∨ q) → r ≡ (p → r) ∧ (q → r)


Using the truth table prove the following logical equivalence.

[∼ (p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


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

∼ (∼ q ∧ p) ∧ q


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) ∧ (p ∧ ∼q)


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 ∨ q) ∧ (~ p ∨ ~ q)


Prepare truth tables for the following statement pattern.

(p ∧ r) → (p ∨ ~ q)


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

(p ∧ ~ q) → (~ p ∧ ~ q)


If p is any statement then (p ∨ ∼p) is a ______.


Show that the following statement pattern is contingency.

p ∧ [(p → ~ q) → q]


Using the truth table, verify

~(p ∨ q) ∨ (~ p ∧ 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 negation of the following statement.

∀ n ∈ N, n + 1 > 0


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

(p → r) ∧ q


With proper justification, state the negation of the following.

(p → 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.


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

[(p ∧ q) ∨ (~p)] ∨ [p ∧ (~ 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) → p] ↔ [(~p) ∧ (~q)]


Using the truth table, prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ 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 ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]


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

Some members of the present Indian cricket are not committed.


Examine whether the statement pattern

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


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


The statement pattern (∼ p ∧ q) is logically equivalent to ______.


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×