Question

Let $G$ be a group of order 2022. Let $H$ and $K$ be the subgroups of $G$ of order 337 and 674, respectively. If $H \cup K$ is also a subgroup of $G$, then which one of the following is FALSE?

• A. H is the normal subgroup of $H \cup K$
• B. The order of $H \cup K$ is 1011
• C. The order of $H \cup K$ is 674
• D. K is a normal subgroup $H \cup K$

Answer 1

Answer: (B)

The order of $H \cup K$ is 1011

Answer 2

The correct option is (B): The order of $H \cup K$ is 1011