Mathematics
Grade9
Easy

Question

Read the following conditional statement: If it is raining, then Kangana has her umbrella up.
Write the inverse of the statement.

  1. If it is not raining, then Kangana has her umbrella up.
  2. If it is not raining, then Kangana does not have her umbrella up.
  3. If Kangana does not have her umbrella up, then it is raining.
  4. If Kangana has her umbrella up, then it is raining.

hintHint:

A statement is a declarative sentence which is either true or false but it can never be both at the same time. A statement can be written in the forms of inverse, converse and contrapositive. Here, we have to write the inverse of the given statement.

The correct answer is: If it is not raining, then Kangana does not have her umbrella up.


    In the question the given statement is " If it is raining, then Kangana has her umbrella up."
    Here, we have to find the inverse of the given statement.
    Let us write the given statement in " if A, then B" form, where A= it is raining and B=  Kangana has her umbrella up.
    Now, the inverse of " if A, then B" will be " if not A, then not B".
    The inverse of the given statement will be " If it is not raining, then Kangana does not has her umbrella up."
    So, the inverse of the given statement will be " If it is not raining, then Kangana does not has her umbrella up."
    Therefore, the correct option is b, i.e., If it is not raining, then Kangana does not has her umbrella up.

    If the statement is in the form “if A, then B” here the converse of the statement will be “if B, then A” whereas in inverse the statement will be “if not A, then not B” and in contrapositive the statement will be “if not B, then not A”.

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