let A={−1, −2,3,4} and B={−1, −2, −3, −4} and define relations R and S from B

to A as follow
x R y iff |𝑥| = |𝑦|
x S y iff x-y is even
state explicity which ordered pairs are in RUS and R ∩ �

impatient much?

Did you know?

Did you know that relations in mathematics can help us understand the relationships between different sets of numbers? In this case, let's consider the sets A={−1, −2, 3, 4} and B={−1, −2, −3, −4}. Now, let's define two relations from set B to set A: R and S. In relation R, an ordered pair (x, y) is included if the absolute value of x is equal to the absolute value of y. In other words, for R to hold true, both x and y must have the same magnitude, regardless of whether they are positive or negative. In relation S, an ordered pair (x, y) is included if the difference between x and y is an even number. This means that if you subtract y from x and the result is divisible by 2 without a remainder, then (x, y) will be in relation S. Now, let's combine these relations using the union symbol (∪) to get RUS. This means that any ordered pair (x, y) will be included in RUS if it satisfies either relation R or relation S. In other words, if the magnitude of x is equal to the magnitude of y or if the difference between x and y is an even number, then (x, y) will be in RUS. To find the set of ordered pairs that are in both relation R and S, we take their intersection using the symbol (∩). The intersection of relation R and relation S will include only those ordered pairs (x, y) that satisfy both conditions: both the magnitude of x is equal to the magnitude of y, and the difference between x and y is an even number. By determining which ordered pairs satisfy these conditions, we can gain a deeper understanding of the relationships and patterns within these sets of numbers.