Let P$($n$)$ be the statement:

If A$1,$ A$2,...,$An and B$1,$ B$2,...,$Bn are sets such that Aj $$ Bj for j $=1,2,3,...,$ n$,$ then $$j$=1$nAj$$j$=1$nAj $$j$=1$nBj$$j$=1$nBj $.$

Identify the proof of the basis step if the given statement is proved by mathematical induction.

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Multiple Choice

A$1$B$1$A$1$B$1$ implies that $$nj$=1$Aj$$nj$=1$Bj$$j$=1$n$$Aj$$j$=1$n$$Bj because the union of one set is itself.

B$1$A$1$B$1$A$1$ implies that $1$j$=1$Aj$1$j$=1$Bj$$j$=11$Aj$$j$=11$Bj because the union of one set is itself.

A$1$B$1$A$1$B$1$ implies that $1$j$=1$Aj$1$j$=1$Bj$$j$=11$Aj$$j$=11$Bj because the union of one set is itself.

Aj$$BjAj$$Bj implies that $1$j$=1$Aj$1$j$=1$Bj$$j$=11$Aj$$j$=11$Bj because the union of one set is itself.

A$1$B$1$A$1$B$1$ implies that $1$j$=1$Aj$1$j$=1$Bj$$j$=11$Aj$$j$=11$Bj because the union of two sets is the larger set.

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