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

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] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.6 | Q 5.1 | पृष्ठ १६

संबंधित प्रश्न

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


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


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.


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


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) ∧ (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 ∨ ∼q) ∨ (∼p ∧ q)] ∧ r


Prove that the following statement pattern is a tautology.

(p ∧ q) → q


Prove that the following statement pattern is a tautology.

(~p ∧ ~q ) → (p → q)


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


Using the truth table, verify.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)


Prove that the following pair of statement pattern is equivalent.

~(p ∧ q) and ~p ∨ ~q


Write the dual of the following:

~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]


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, (n2 + 2) is odd number.


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

~(p ∨ q) → r


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) ∨ (~p)] ∨ [p ∧ (~ q)]


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) → p] ↔ [(~p) ∧ (~q)]


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

[p → (~q ∨ r)] ↔ ~[p → (q → r)]


Using the truth table, prove the following logical equivalence.

p ∧ (~p ∨ q) ≡ p ∧ q


Using the truth table, prove the following logical equivalence.

~p ∧ q ≡ [(p ∨ q)] ∧ ~p


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

2 is even number or 9 is a perfect square.


Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


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

Some members of the present Indian cricket are not committed.


Choose the correct alternative:

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


Examine whether the statement pattern

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


The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______. 


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


Show that the following statement pattern is a contingency:

(p→q)∧(p→r)


If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______


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×