Question

If
B=ab
such that a, b are integers , then B is a set of _____numbers

Answer 1

Answer on Question #61795 – Math – Abstract Algebra

Question

If $B = ab$ such that $a, b$ are integers, then $B$ is a set of ______ numbers

Solution

Since we can take $a = 1$ and $b$ is any integer, then the set of all integers is a subset of $B$.

Let $x \in B$ be non-integer. According to the definition of $B$ ($B = ab$ such that $a, b$ are integers), there exist such integers $a, b$ that $x = ab$. But the product of integers is integer too. Thus, every $x \in B$ is integer.

**Answer**: If $B = ab$ such that $a, b$ are integers, then $B$ is a set of integer numbers.

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