Select the set that corresponds to the relation given in the matrix below. Rows of the matrix are numbered 1 through 4 from top to bottom and columns are numbered 1 through 4 from left to right.

Question

BlackTom AI · Accepted Answer

An entry of 1 in row i and column j corresponds to the ordered pair (i, j) in the relation; a 0 means that ordered pair is not in the relation.

1) Relevant concepts
- A relation on a set represented by an adjacency matrix uses row index as the first coordinate and column index as the second coordinate.
- To read the relation, scan the matrix row by row and record (row, column) whenever the entry = 1.

2) Step-by-step reading of the matrix
- Row 1 (top row): entries across columns 1–4 are 0, 1, 0, 0. The 1 is in column 2, so include (1,2).
- Row 2: entries across columns 1–4 are 0, 0, 1, 1. The 1s are in columns 3 and 4, so include (2,3) and (2,4).
- Row 3: entries across columns 1–4 are 0, 0, 1, 0. The 1 is in column 3, so include (3,3).
- Row 4: entries are 0, 0, 0, 0 so no pairs from row 4.

3) Intermediate listing of pairs
- From row 1: (1,2)
- From row 2: (2,3), (2,4)
- From row 3: (3,3)
- Combined relation set: {(1,2), (2,3), (2,4), (3,3)}

4) Why the correct answer is correct
- This set exactly matches the locations of 1s in the matrix when using (row, column) indexing. Each ordered pair corresponds to a single 1 entry and there are no extra or missing pairs.

5) Why the other options are incorrect (brief)
- Option A: {(2,1),(2,2),(3,3),(4,2)} contains pairs like (2,1),(2,2),(4,2) that do not correspond to 1s in the matrix.
- Option C: {(1,2),(2,2),(2,4),(3,3)} incorrectly includes (2,2) instead of (2,3).
- Option D: {(2,1),(2,2),(3,3),(3,4)} includes incorrect pairs (2,1),(2,2),(3,4) that are 0 entries.

6) Conclusion
The relation read from the matrix is {(1,2),(2,3),(2,4),(3,3)}, which matches the provided correct answer.

Select the set that corresponds to the relation given in the matrix below. Rows of the matrix are numbered 1 through 4 from top to bottom and columns are numbered 1 through 4 from left to right.Single choice

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