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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
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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
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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 ↔ q
Write the following sentences in symbolic form using statement variables p and q.
19 is not a prime number and all the angles of a triangle are equal
Write the following sentences in symbolic form using statement variables p and q.
19 is a prime number or all the angles of a triangle are not equal
Write the following sentences in symbolic form using statement variables p and q.
19 is a prime number and all the angles of a triangle are equal
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Determine the truth value of the following statement.
11 is a prime number and all the sides of a rectangle are equal
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¬(P ∧ ¬q)
Construct the truth table for the following statement.
(p v q) v ¬q
Show that ¬(p → q) ≡ p ∧¬q
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Show that p → q and q → p are not equivalent
Check whether the statement p → (q → p) is a tautology or a contradiction without using the truth table
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Choose the correct alternative:
Which one of the following statements has truth value F?
Choose the correct alternative:
The truth table for (p ∧ q) v ¬q is given below
| p | q | (p ∧ q) v ¬q |
| T | T | (a) |
| T | F | (b) |
| F | T | (c) |
| F | F | (d) |
Which one of the following is true?
Choose the correct alternative:
Which one of the following is incorrect? For any two propositions p and q, we have
Choose the correct alternative:
The proposition p∧(¬p∨q)] is
