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प्रश्न
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
संबंधित प्रश्न
Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.
[~(~p ∧ ~q)] v q
Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p
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The angle is right angle if and only if it is of measure 90°.
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(p ∧ q) ↔ (q ∨ r)
Construct the truth table of the following statement pattern.
(∼ p → ∼ q) ∧ (∼ q → ∼ p)
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[p → (q → r)] ↔ [(p ∧ q) → r]
Construct the truth table of the following statement pattern.
(p ∨ ∼ q) → (r ∧ p)
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∧ q) is T
Express the following statement in symbolic form.
Mango is a fruit but potato is a vegetable.
Express the following statement in symbolic form.
I like playing but not singing.
Write the truth value of the following statement.
Earth is a planet and Moon is a star.
Write the truth value of the following statement.
A quadratic equation has two distinct roots or 6 has three prime factors.
Write the negation of the following statement.
2 + 3 ≠ 5
Write the truth value of the negation of the following statement.
For every x ∈ N, x + 3 < 8.
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It is not true that 3 − 7i is a real number.
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If p and q are true and r and s are false, find the truth value of the following compound statement.
~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ q]
Assuming that the following statement is true,
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q : Ram does not study on holiday,
find the truth values of the following statements.
Sunday is a holiday and Ram studies on holiday.
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement:
p ↔ ~ q
If p : He swims
q : Water is warm
Give the verbal statement for the following symbolic statement.
q ∧ ~ p
State whether the following statement is True or False:
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Assuming the first statement p and second as q. Write the following statement in symbolic form.
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If p : Proof is lengthy.
q : It is interesting.
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If proof is lengthy then it is interesting.
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If price increases, then demand falls.
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If demand falls, then price does not increase.
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10 > 5 and 3 < 8
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Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
Write the negation of p → q
Choose the correct alternative:
A biconditional statement is the conjunction of two ______ statements
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The statement ∼(p ↔ ∼q) is ______.
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(p `→` ∼ r) `→` (q ∧ s)
