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State the dual of the following statement by applying the principle of duality. (p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q) - Mathematics and Statistics

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प्रश्न

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

(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)

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उत्तर

(p ∨ ~q) ∧ (~ p ∨ q) ≡ (p ∧ q) ∨ ~(p ∨ q)

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पाठ 1: Mathematical Logic - Miscellaneous Exercise 1 [पृष्ठ ३३]

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बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.16 | पृष्ठ ३३

संबंधित प्रश्‍न

Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "


Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)


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


Write the dual of the following statements: (p ∨ q) ∧ T


If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧  ∼ r ) ∧ ( ∼ q ∧ s )


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


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."


Using the truth table prove the following logical equivalence.

(p ∨ q) → r ≡ (p → r) ∧ (q → r)


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

(p ∧ q) → (q ∨ p)


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

∼ (∼ q ∧ p) ∧ q


(p ∧ q) → r is logically equivalent to ________.


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 → r)] ↔ [(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.

(~ q ∧ p) ∧ (p ∧ ~ p)


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

(p ∧ ~ q) → (~ 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 tautology.

(p ∧ q) → q


Prove that the following statement pattern is a tautology.

(p → q) ↔ (~ q → ~ p)


Prove that the following statement pattern is a tautology.

(~p ∧ ~q ) → (p → q)


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


Show that the following statement pattern is contingency.

(p → q) ∧ (p → r)


Using the truth table, verify

p → (p → q) ≡ ~ q → (p → q)


Using the truth table, verify

~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Write the dual statement of the following compound statement.

13 is prime number and India is a democratic country.


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

~(p ∨ q) → r


With proper justification, state the negation of the following.

(p → q) ∧ r


Construct the truth table for the following statement pattern.

(p ∨ ~q) → (r ∧ p)


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

If a man is bachelor, then he is happy.


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


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`


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


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