# A collection of numbers T is defined recursively by: 2 belongs to T If X belongs to T, so does X+3 and 2*X Which of the following belongs to T? 6, 7, 12

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### 1 Answer

We can determine which numbers belong to T by evaluating the recursive tree that starts with 2.

Since 2 belongs to T, then we know that 2+3=5 and 2*2=4 also belong to T.

Furthermore, this also means that since 5 belongs to T, so does 5+3=8 and 2*5=10.

Since 4 belongs to T, so does 4+3=7 and 2*4=8.

Since 7 belongs to T, so does 7+3=10 and 2*7=14.

Since 8 belongs to T, so does 8+3=11 and 2*8=16.

Since 10 belongs to T, so does 10+3=13 and 2*10=20.

**Out of the numbers 6, 7 and 12, only 7 belongs to T.**