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The image contains a problem involving relations on the Cartesian product \( A \times B \), where \( A = \{a, b, c, d\} \) and \( B = \{p, q, r, s\} \). The problem provides four relations \( R_1, R_2, R_3, \) and \( R_4 \) defined as follows:

- \( R_1 = \{(a, p), (c, r), (d, q)\} \)
- \( R_2 = \{(a, s), (b, s), (c, p), (d, r)\} \)
- \( R_3 = \{(a, p), (b, p), (b, s), (d, q)\} \)
- \( R_4 = \{(a, r), (b, r), (c, q), (d, s)\} \)

The question asks which of the given statements about these relations are correct.

Since the statements to be verified are not visible in the image you provided, I can analyze the given relations and provide general insights into properties like reflexivity, symmetry, transitivity, etc., which are common in questions like this.

Would you like to proceed with this analysis, or could you provide more information about the specific statements that need verification?

Explore the properties of relations defined on the Cartesian product A × B, where A = {a, b, c, d} and B = {p, q, r, s}. This analysis covers the concepts of reflexivity, symmetry, and transitivity in relation theory. Suitable for high school students and those preparing for mathematical competitions.

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