Question

Closure property is observed w.r.t. ____ operations in integers.

• A. $+,\times$
• B. $+,÷,\times$
• C. $+,\times ,-$
• D. $+,-,÷$

Answer 1

Answer: (C)

$+,\times ,-$

Closure property under addition and subtraction states that the sum or difference of any two integers will always be an integer i.e. if $x$ and $y$ are any two integers, then $x+y$ and $x-y$ will also be an integer. For example:

$3-4=3+(-4)=-1$

The result is an integer.

Closure property under multiplication states that the product of any two integers will be an integer i.e. if $x$ and $y$ are any two integers, then $x\times y$ will also be an integer. For example:

$(-5)\times 3=-15$

The result is an integer.

Division of integers doesn’t follow the closure property, i.e. the quotient of any two integers $x$ and $y$, may or may not be an integer. For example:

$(-3)÷(-6)=\frac{1}{2}$

The result is not an integer.

Hence, closure property is observed w.r.t. $+,\times ,-$ in integers.