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Set $A$ consists of a group of seven numbers. Set $B$ is created by adding $ 1 $ to each of the numbers from set $A$.

Which of the following must be a true statement?

The mean, median, and mode of set B are each $ 1 $ greater than the mean, median, and mode of set $A$.

Only the mean and median of set $B$ are each $1$ greater than the mean and median of set $A$.

Only the median and mode of set $B$ are each $1$ greater than the median and mode of set $A$.

Only the mean and mode of set $B$ are each $1$ greater than the mean and mode of set $A$.