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प्रश्न
Write the converse, inverse, and contrapositive of the following implication.
If x and y are numbers such that x = y, then x2 = y2
उत्तर
Converse: If x and y are numbers such that x2 = y2 then x = y.
Inverse: If x and y are numbers such that x ≠ y then x2 ≠ y2.
Contrapositive: If x and v are numbers such that x2 ≠ y2 then x ≠ y.
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संबंधित प्रश्न
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
¬ P
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
P ∧ ¬q
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
¬p v q
Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.
p → ¬q
Determine the truth value of the following statement.
It is not true that 5 + 5 = 9 or Earth is a planet
Which one of the following sentences is a proposition?
3n ≤ 81, n ∈ N
Construct the truth table for the following statement.
¬(P ∧ ¬q)
Construct the truth table for the following statement
(¬p → r) ∧ (p ↔ q)
Verify whether the following compound propositions are tautologies or contradictions or contingency.
(p ∧ q) ∧¬ (p v q)
Show that (p ∧ q) ≡ ¬p v ¬q
Show that ¬(p → q) ≡ p ∧¬q
Show that ¬(p ↔ q) ≡ p ↔ ¬q
Prove p → (q → r) ≡ (p ∧ q) → r without using the truth table
Prove that p → (¬q v r) ≡ ¬p v (¬q v r) using truth table
Choose the correct alternative:
Which one of the following statements has the truth value T?
Choose the correct alternative:
Which one is the inverse of the statement (p v q) → (p ∧ q)?
Choose the correct alternative:
The dual of ¬(p v q) v [p v(p ∧ ¬r)] is
Choose the correct alternative:
The proposition p∧(¬p∨q)] is
Choose the correct alternative:
Determine the truth value of each of the following statements:
(a) 4 + 2 = 5 and 6 + 3 = 9
(b) 3 + 2 = 5 and 6 + 1 = 7
(c) 4 + 5 = 9 and 1 + 2 = 4
(d) 3 + 2 = 5 and 4 + 7 = 11
