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Write the inverse of the following conditional statement and determine its truth value.

If a number is divisible by 15, then it is divisible by 5.

User Naoe
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Final answer:

The inverse of the statement is 'If a number is not divisible by 15, then it is not divisible by 5,' which is false since a number can be divisible by 5 without being divisible by 15.

Step-by-step explanation:

To find the inverse of the conditional statement 'If a number is divisible by 15, then it is divisible by 5', we first need to understand what an inverse of a conditional statement is. It involves taking the negation of both the hypothesis and the conclusion of the original conditional. Therefore, the inverse would be: 'If a number is not divisible by 15, then it is not divisible by 5.'

The next step is to determine the truth value of this inverse statement. We know that a number divisible by 15 is always divisible by 5 because 15 is a multiple of 5. However, a number not divisible by 15 could still be divisible by 5; take for example the number 10. It is not divisible by 15 but is divisible by 5. Thus, the inverse statement is false.

User Vkrishna
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