Question

The negative of the proposition "If a number is divisible by $15,$ then it is divisible by $5$ or $3".$ is

• A. If a number is divisible by $15,$ then it is not divisible by $5$ and $3$
• B. A number is divisible by $15$ and it is not divisible by $5$ and $3$
• C. A number is divisible by $15$ and it is not divisible by $5$ or $3$
• D. A number is not divisible $15$ or it is not divisible by $5$ and $3$

Answer 1

The correct option is A If a number is divisible by $15,$ then it is not divisible by $5$ and $3$

The negation of "if $A$ then $B$" becomes "$A$ and not $B$"

$A:$ a number divisible by $15$

$B:$ divisible by $5$ or $3$

Hence the negation of the proposition

"If a number is divisible by $15$, then it is divisible by $5$ and $3$" is

"$A$ number is divisible by $15$ and it is not divisible by $5$ and $3$"

Correct answer : Option A