If A={a:a∈N and −2≤a≤5} and B={b:b∈Z and 0≤b≤3} then number of elements of in set B×A
Answers
Answer:
hi friends
Step-by-step explanation:
The topic of our next chapter is relations, it is about having 2 sets, and
connecting related elements from one set to another.
Definition 53. Let A and B be two sets. A binary relation R from A to B
is a subset of the cartesian product A × B. Given x, y ∈ A × B, we say that
x is related to y by R, also written (xRy) ↔ (x, y) ∈ R.
Example 84. Suppose that you have two sets A = {1, 2} and B = {1, 2, 3},
and the relation is given by (x, y) ∈ R ↔ x − y is even. Since the relation is
a subset of A × B, we start by computing the cartesian product A × B:
A × B = {(1, 1),(1, 2),(1, 3),(2, 1),(2, 2),(2, 3)}.
Then in this list of pairs, we select those which satisfy the relation R. For
example, for (1, 2), we have x = 1 and y = 2, we compute x−y = 1−2 = −1,
which is odd, thus it does not belong to R. We try out similarly all the pairs
in A × B to get
R = {(1, 1),(1, 3),(2, 2)}.
This may be visualized using a diagram: draw a circle to represent the set
A, and this circle contains two points, one for 1 and one for 2. Similarly,
draw a circle to represent B, and points of 1, 2, 3. Then an a