हिंदी

Construct the truth table for the following statement pattern. (~p ∨ q) ∧ (~p ∧ ~q) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Construct the truth table for the following statement pattern.

(~p ∨ q) ∧ (~p ∧ ~q)

योग

उत्तर

p q ~p ~q ~p∨q ~p∧~q (~p∨q)∧(~p∧~q)
T T F F T F F
T F F T F F F
F T T F T F F
F F T T T T T
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
अध्याय 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.11 | पृष्ठ ३३

संबंधित प्रश्न

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


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


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


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


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 ∨ 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 → q) ∧ (p → 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


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.

[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]


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

[(p ∧ (p → q)] → q


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

[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r


Prepare truth tables for the following statement pattern.

p → (~ p ∨ q)


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

~ p → (p → ~ q)


Prove that the following statement pattern is a contradiction.

(p ∨ q) ∧ (~p ∧ ~q)


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


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]


Using the truth table, verify

p → (p → q) ≡ ~ q → (p → q)


Using the truth table, verify

~(p → ~q) ≡ p ∧ ~ (~ q) ≡ p ∧ q


Write the dual of the following:

(p ∨ q) ∨ r


Write the dual of the following:

~(p ∨ q) ∧ [p ∨ ~ (q ∧ ~ r)]


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

(~p ∧ q) ∧ (~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)]


Using the truth table, prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)


Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”


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.


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


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


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


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 ______


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×