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Correct Answer: * > <
to determine the next set in this sequence, we need to understand the pattern in which the symbols are rotated or rearranged within each set. observing the progression provided, we can see how the symbols are manipulated:
1. start with the set: `* > <`
2. the next set is obtained by moving the first symbol of the previous set to the last position, resulting in: `> < *`
3. applying the same rule again, the next set becomes: `< * >`
4. continuing this pattern, the next set after `< * >` is derived by moving the first symbol (`<`) to the last position, which results in: `* > <`
thus, the sequence repeats every three steps, as the symbols rotate positions in a cyclical manner. the original sequence given is:
- `* > <`
- `> < *`
- `< * >`
following the pattern where we move the first symbol to the last position, the set after `< * >` would logically be `* > <`.
### detailed explanation of the pattern:
the sequence involves a simple cyclic permutation where each symbol shifts one place to the right in each subsequent set. here’s the breakdown:
- in the first set `* > <`, the asterisk `*` is in the first position.
- in the next set `> < *`, the asterisk `*` moves to the third (or last) position, while `>` moves to the first position and `<` to the second.
- in the following set `< * >`, the asterisk `*` is now in the second position. the symbol `<` moves to the first position, and `>` goes to the third.
- reapplying the pattern, the asterisk `*` will move again to the first position in the next sequence, thus recreating the first set `* > <`.
### conclusion:
based on the pattern observed, where each symbol is rotated to the right, the next set after `< * >` in the sequence is indeed `* > <`. this confirms that the sequence is cyclic with a period of three sets before it repeats.
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