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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
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उत्तर
Contrapositive
APPEARS IN
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)
