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Write the dual of the following. (p ∧ q) ∧ r ≡ p ∧ (q ∧ r) - Mathematics and Statistics

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प्रश्न

Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)

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उत्तर

(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

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

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बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.18 | पृष्ठ ३३

संबंधित प्रश्‍न

Prove that the following statement pattern is equivalent :

(p ∨ q) →  r and (p → r) ∧ (q → r)


Express the following statement in symbolic form and write its truth value.
"If 4 is an odd number, then 6 is divisible by 3."


Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1


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."


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 ∧ 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.

(p ↔ q) ∧ (p → ∼ q)


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

[p → (q → r)] ↔ [(p ∧ q) → r]


Prove that the following statement pattern is a tautology.

(~p ∧ ~q ) → (p → q)


Prove that the following statement pattern is a tautology.

(~ p ∨ ~ q) ↔ ~ (p ∧ q)


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p


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


Prove that the following statement pattern is a contradiction.

(p → q) ∧ (p ∧ ~ q)


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


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) ∨ (p → r)


Construct the truth table for the following statement pattern.

(p ∨ r) → ~(q ∧ r)


Write the dual of the following.

(~p ∧ q) ∨ (p ∧ ~q) ∨ (~p ∧ ~q)


Write the converse and contrapositive of the following statements.

“If a function is differentiable then it is continuous”


Choose the correct alternative:

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


Using truth table verify that:

(p ∧ q)∨ ∼ q ≡ p∨ ∼ q


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

(p ∧ q) → (q ∨ p)


In the triangle PQR, `bar(PQ) = 2bara and bar(QR)` = `2 bar(b)` . The mid-point of PR is M. Find following vectors in terms of `bar(a) and bar(b)` .

  1. `bar(PR)`  
  2. `bar(PM)`
  3. `bar(QM)`

If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].


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