Let G be a group and let H and K be subgroups of G. Prove that H∪K is a subgroup of G if and only if H ⊆ K or K ⊆ H.© BrainMass Inc. brainmass.com December 24, 2021, 6:30 pm ad1c9bdddf
"<=": If H ⊆ K, then H∪K=K. Since K is a subgroup of G, then H∪K is a subgroup of G.
If K ⊆ H, then H∪K=H. Since H is a subgroup of G, then H∪K is a ...
Groups and subgroups are investigated.