dw15-7 This is Daily Work 15. Current Students: Enter your BSU email address to receive a copy of your responses. Let \(H\) be a subgroup of \(G\) and suppose \(a,b\in G\) are elements of \(G\).Which is not necessarily true? The coset \(aH\) has the same elements as \(Ha\). The coset \(aH\) has the same number of elements as \(H\). The coset \(aH\) has the same number of elements as \(Ha\). The coset \(aH\) has the same number of elements as \(bH\). Let \( H\) be a subgroup of \(G\), and suppose \(a\in G\) is an element.Which of the following sets is not guaranteed to be a subgroup of \(G\)? \(aHa^{-1}\) \(Ha\), if \(a\) is an element of \(H\) \(aHa\) \(aH\), if \(a\) is an element of \(H\) Let \(H_1,H_2\) be two distinct subgroups of a group \(G\), and let \(a \in G\) be an element.Under what circumstances can we have \( aH_1 = H_2 \), that is, when can a left coset of one subgroup be equal to a different subgroup? If \(H_1\) and \(H_2\) have the same order. If \(a\) is an element of \(H_2\). If \(a\) is an element of \( H_1 \cap H_2\). This is never possible. Related