Mathematics for Data Science 1 (BSMA1001) PYQs

Let $S = \{1, 2, 3, 4, 5\}$ and $R_2$ be a relation on $S$ defined by $R_2 = \{(x, y) \in S imes S : x + y = 6\}$. Find the cardinality of the set $(S \times S) \setminus R_2$.

Suppose A = {a, b, c, d} and B = {p, q, r, s} are two sets. Consider the following relations from A to B:

R1 = {(a, p), (c, r), (d, q)} R2 = {(a, s), (b, s), (c, p), (d, r)} R3 = {(a, p), (b, r), (b, s), (d, q)} R4 = {(a, r), (b, p), (c, q), (d, s)}

Which of the following statements are correct?

Let S = {Jan, Feb, March, April, May} be a set of months of a particular year. Consider the following relations on the set S: R1 = { (Feb, Feb), (March, April), (April, March), (March, March) } and R2 = { (Jan, Jan), (Feb, Feb), (March, March), (April, April), (May, May) }. Which of the following is true regarding R1?