Advertisement Remove all ads

Write converse, inverse and contrapositive of the following statement. If x < y then x2 < y2 (x, y ∈ R) - Mathematics and Statistics

Sum

Write converse, inverse and contrapositive of the following statement.

If x < y then x2 < y2 (x, y ∈ R)

Advertisement Remove all ads

Solution

Let p: x < y,
      q: x2 < y2
Then the symbolic form of the given statement is p → q.
Converse: q → p is the converse of p → q.
i.e. If x2 < y2, then x < y.
Inverse: ∼ p  → ∼ q is the inverse of p → q.
i.e. If x `≥` y, then x2 `≥` y2.
OR
If x `≮` y, then x2 `≮` y2.
Contrapositive: ∼ q → p is the contrapositive of p → q
i.e. If x2 `≥` y2, then x `≥` y.
OR
If x2 `≮` y2, then x `≮` y.

Concept: Converse, Inverse, and Contrapositive
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×