Question

let B = {2,4,6,8,10}, C={4,8,10}, and D={x|x is even}. answer the following questions. give reason for your answers.
a. Is D⊆ B?
b. Is C ⊆ D?
c. Is C ⊆ B?
d. Is B a proper subset of D?

Answer 1

If A is a subset of B, then A is contained in B. It implies that B contains A, or in other words, B is a superset of A. We write A ⊇ B to denote that B is a superset of A. For an example, A = {2, 5} is a subset of B = {2, 3, 5}, since all the elements in A contained in B.

A subset of a set A that is not equal to A is called a proper subset. To put it another way, if B is a proper subset of A, then all of B's items are in A, but A has at least one member that isn't in B.

For example, if A={2,4,5} then B={2,5} is a proper subset of A.

Given:

$B = \left\{2,4,6,8,10 \right\} \\C=\left\{4,8,10 \right\}\\D=\left\{x|x is even \right\}$

$D=\left\{ 2,4,6,8,10,................\right\}$

(a) All elements of B are in D. Hence, B is subset of D.

So, D is not subset of B.

Statement$D \subseteq B$ is wrong.

(b) All elements of C are in D. Hence C is subset of D.

Statement $C \subseteq D$ is correct.

(c) All elements of C are in B. Hence C is subset of B.

Statement $C \subseteq B$ is correct.

(d) All elements of B are in D. So B is a proper subset of D.

Statement 'B a proper subset of D' is correct