Question

Consider the sets given below:
A = {..., -3, -2, -1, 0, 1, 2, 3, ...}
B = {..., -10, -5, 0, 5, 10, 15, ...}
C = {..., -8, -4, 0, 4, 8, ...}
D = {1, 2, 3, ...}

Which of the following statements are true. Give reason.
(i) A is subset of A ∪ D.
(ii) D is subset of B ∪ C
$\left[2\right]$

Answer 1

Solution:
(i) A = {..., -3, -2, -1, 0, 1, 2, 3,...}
D = {1, 2, 3,...}

A ∪ D = {..., -3, -2, -1, 0, 1, 2, 3,...} = A
As A ∪ D = A and every set is a subset of itself, therefore, A is subset of A ∪ D.

Hence, the given statement is true.
[1 Mark]

(ii) D = {1, 2, 3,...}
B ∪ C = {.....-10, -8, -5, -4, 0, 4, 5, 8, 10, 12, 15,....}
<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\therefore$ D is not a subset of B ∪ C.

Hence, the given statement is false.
[1 Mark]