Question: True or false? If A is regular and A B than B must be regular; If A and AB are both regular then B must

True or false? If A is regular and A B than B must be regular; If A and AB are both regular then B must be regular; If {Ai|i belongs to N} is an infinite family of regular sets then union Ai is regular; If A is not regular it cannot have a regular subset.
True or false? If A is regular and A B than B

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