Kenneth Rosen Edition 7 Exercise 2.1 Question 6 (Page No. 125)

Question

Suppose that $A=$ { $2,4,6$ }, $B=$  { $2,6$ }, $C=$ { $4,6$ }, and $D=$ { $4,6,8$ }. Determine which of these sets are subsets of which other of these sets.

Answer 1

$ A=\left\{2,4,6\right\}$,

$B=\left\{2,6\right\}$,

$C=\left\{4,6\right\}$,

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

set $A$ is said to be subset of $B$ if and only if every elements of $A$ is also an elements of $B$. That is:

$A\subseteq B=\forall x(x\in A\to x\in B)$

So

1) Every elements of B is also an elements of A so $B\subseteq A$

2) Every elements of C is also elements of A so $C\subseteq A$

3) Every elements of C is also an elements of D so $C\subseteq D$