Question

The converse of ‘If x is zero then we cannot divide

by x’ is :

(a) If we cannot divide by x then x is zero

(b) If we divide by x then x is non-zero

(c) If x is non-zero then we can divide by x.

(d) If we cannot divide by x then x is non-zero.​

Answer 1

The converse of ‘If x is zero then we cannot divide by x’ is :

(a) If we cannot divide by x then x is zero❌

(b) If we divide by x then x is non-zero❌

(c) If x is non-zero then we can divide by x. ✔

(d) If we cannot divide by x then x is non-zero.❌

Answer 2

Answer:

Option (b) is the converse of the given statement.

Step-by-step explanation:

Statement: If $x$ is $zero$ then we cannot divide by $x$.

(a) If $x=0$.

Then,

The number $x$ cannot divide any number.

As $\frac{y}{0}$ is indeterminant form.

This implies we cannot divide by $x$ then $x$ must be zero.

Thus, option (a) is not the converse of the given statement.

(b) If $x$ is non-zero.

Then any number can be divided by the number $x$ if the GCD of the both the numbers is not equal to $1$.

⇒ If we divide by $x$ then $x$ is non-zero.

Thus, option (b) is the converse of the given statement.

(c) If $x$ divides a certain number.

This implies $x$ cannot be zero. As denominator cannot be zero.

Hence if $x$ is non-zero then we can divide by $x$.

Thus, option (c) is not the converse of the given statement.

(d) If $x$ is non-zero.

Then any non-zero number $x$ cannot divide the number $x$ if the GCD of the both the numbers is equal to $1$.

Thus, if we cannot divide by $x$ then $x$ is non-zero.​

Hence, option (d) is not the converse of the given statement.

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