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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Choose the correct alternative: If p → q is an implication , then the implication ~q → ~p is called its - Mathematics and Statistics

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प्रश्न

Choose the correct alternative:

If p → q is an implication, then the implication ~q → ~p is called its

पर्याय

  • Converse

  • Contrapositive

  • Inverse

  • Alternative

MCQ
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उत्तर

Contrapositive

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पाठ 1.1: Mathematical Logic - Q.1

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 "


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.” 


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


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


Using the truth table prove the following logical equivalence.

∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p


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.

[(p → q) ∧ ∼ q] → ∼ p


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) ∧ (p ∧ ∼q)


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

(p → q) ∨ (q → p)


Prove that the following statement pattern is a tautology.

(p → q) ↔ (~ q → ~ p)


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Write the dual of the following:

(p ∨ q) ∨ r


Write the dual of the following:

~(p ∧ q) ≡ ~ p ∨ ~ q


Write the negation of the following statement.

∃ n ∈ N, (n2 + 2) is odd number.


Write the negation of the following statement.

Some continuous functions are differentiable.


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

(p → r) ∧ q


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

If he studies, then he will go to college.


With proper justification, state the negation of the following.

(p → q) ∨ (p → 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) ∧ (q ∧ r)] ∨ (~q)


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

[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]


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

p ∨ (q ∨ r) ≡ ~[(p ∧ q) ∨ (r ∨ s)]


Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


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


Which of the following is not true for any two statements p and q?


Show that the following statement pattern is a contingency:

(p→q)∧(p→r)


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