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Question Number 76328 by arkanmath7@gmail.com last updated on 26/Dec/19

Commented by arkanmath7@gmail.com last updated on 26/Dec/19

sol. plz

sol.plz

Commented by kaivan.ahmadi last updated on 26/Dec/19

1) aa^(−1) =1∈H⇒a≡a^(−1) 2)if a≡b⇒ab^(−1) ∈H⇒ ba^(−1) ab^(−1) =1∈H⇒ba^(−1) ∈H⇒b≡a 3)if a≡b and b≡c⇒ab^(−1) ∈H and bc^(−1) ∈H⇒ ac^(−1) =ab^(−1) bc^(−1) ∈H⇒a≡c

1)aa−1=1∈H⇒a≡a−12)ifa≡b⇒ab−1∈H⇒ba−1ab−1=1∈H⇒ba−1∈H⇒b≡a3)ifa≡bandb≡c⇒ab−1∈Handbc−1∈H⇒ac−1=ab−1bc−1∈H⇒a≡c

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