Advertisements
Advertisements
Question
Write the converse, inverse, and contrapositive of the following implication.
If x and y are numbers such that x = y, then x2 = y2
Solution
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.
APPEARS IN
RELATED QUESTIONS
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
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
Determine the truth value of the following statement.
China is in Europe dr `sqrt(3)` is art integer
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
Which one of the following sentences is a proposition?
Peacock is our national bird
Which one of the following sentences is a proposition?
How tall this mountain is!
Write the converse, inverse, and contrapositive of the following implication.
If a quadrilateral is a square then it is a rectangle
Construct the truth table for the following statement.
¬P ∧ ¬q
Verify whether the following compound propositions are tautologies or contradictions or contingency.
(p → q) ↔ (¬p → q)
Verify whether the following compound propositions are tautologies or contradictions or contingency.
((p → q) ∧ (q → r)) → (p → r)
Show that (p ∧ q) ≡ ¬p v ¬q
Show that ¬(p → q) ≡ p ∧¬q
Using the truth table check whether the statements ¬(p v q) v (¬p ∧ q) and ¬p are logically equivalent
Choose the correct alternative:
Which one of the following statements has truth value F?
Choose the correct alternative:
In the last column of the truth table for ¬(p v ¬q) the number of final outcomes of the truth value ‘F’ is
Choose the correct alternative:
| p | q | (p ∧ q) → ¬p |
| T | T | (a) |
| T | F | (b) |
| F | T | (c) |
| F | F | (d) |
Which one of the following is correct for the truth value of (p ∧ q) → ¬p
