Question

The negative of the statement “If a number is divisible by 15 then it is divisible by 5 or 3”.
A. If a number is divisible by 15 then it is not divisible by 5 or 3.
B. a number is divisible by 15 and it is not divisible by 5 or 3.
C. a number is divisible by 15 or it is not divisible by 5 or 3.
D. a number is divisible by 15 and it is not divisible by 5 or 3.

Answer 1

Hint: The statement given to us is a positive statement as there are no negative words used in the statement. When we convert a positive statement to a negative statement, we first look at the condition given which is “If a number is divisible by 15…” then following this condition the statement will be written opposite to what it is given in the statement and that is “…then it is not divisible by 5 or 3”.

Complete step by step solution:
A positive statement is one which goes well with all the facts existing. A negative statement is nothing but the wrong interpretation of the facts available and contains words that negate or contradict a condition in the statement.
According to the question, we have to negate the statement given,
The statement starts with a condition that is “If a number is divisible by 15 then it is divisible by 5 or 3” this means that number which is divisible by 15 is also divisible by its factors. As we know,
\[15=3\times 5\]
So the number which is divisible by 15 will also be divisible by 3 and 5. Let’s say we have number 225,
225 is divisible by 15 as \[225=15\times 15\], and since the number 225 ends with the digit 5 so, the number 225 is also divisible by 5. To check the divisibility of a number by 3, we add up the digits in the number i.e \[225=2+2+5=9\] which is divisible by 3. So considering all the facts the statement is true.
Now, to negate the statement we just need to add a ‘not’ in the statement. So, the negative statement will be like “If a number is divisible by 15 then it is not divisible by 5 or 3”.
Therefore, the answer is A. If a number is divisible by 15 then it is not divisible by 5 or 3.

Note: The negative statement should not be confused with the use of other conjunctions (like and, or). It cannot be “a number is divisible by 15 and it is not divisible by 5 or 3” as the statement now has two independent statements which are joined together with the use of ‘and’ which is not the negative of the given statement.
And also it cannot be “a number is divisible by 15 or it is not divisible by 5 or 3” as the statement now offers a choice to take either the first statement or the second statement which is not the negative of the given statement.