Show that subtraction and division are not binary operations on the set of natural numbers $N$.
$A$ binary operation $*$ on a set $S$ is a function $*: S \times S \rightarrow S$. This means that for every pair $(a, b) \in S \times S$,the result $a * b$ must also be in $S$.
$1$. For subtraction $(-)$ on $N$:
Consider the elements $a = 3$ and $b = 5$,where $3, 5 \in N$.
The operation $a - b$ gives $3 - 5 = -2$.
Since $-2 \notin N$,subtraction is not a binary operation on $N$.
$2$. For division $(\div)$ on $N$:
Consider the elements $a = 3$ and $b = 5$,where $3, 5 \in N$.
The operation $a \div b$ gives $3 \div 5 = \frac{3}{5}$.
Since $\frac{3}{5} \notin N$,division is not a binary operation on $N$.
$1$. For subtraction $(-)$ on $N$:
Consider the elements $a = 3$ and $b = 5$,where $3, 5 \in N$.
The operation $a - b$ gives $3 - 5 = -2$.
Since $-2 \notin N$,subtraction is not a binary operation on $N$.
$2$. For division $(\div)$ on $N$:
Consider the elements $a = 3$ and $b = 5$,where $3, 5 \in N$.
The operation $a \div b$ gives $3 \div 5 = \frac{3}{5}$.
Since $\frac{3}{5} \notin N$,division is not a binary operation on $N$.
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