Question

Select which of the following pair of sets are equivalent sets.

• A. $\{2,10,15,20\}\&\{10,20,15,2\}$
• B. $\{a,b,c,d,e\}\&\{a,c,d,e,a\}$
• C. $\{x:x\text{is a positive multiple of 7}\}$ and $\{7,14,21,28,...\}$

Answer 1

Answer: (A), (C)

$\{x:x\text{is a positive multiple of 7}\}$ and $\{7,14,21,28,...\}$

We know two sets are equal if they have same elements.
While two sets are equivalent if they have same cardianality.
Let's take the pairs one by one.

$A.\{2,10,15,20\}\&\{10,20,15,2\}$

Here, if we re-arrange the second set, we get them as:
$\{2,10,15,20\}$ which is identical to the first set.
This means that the two sets are equal and hence equivalent as well.

$B.\{a,b,c,d,e\}\&\{a,c,d,e,a\}$

Here, removing the duplicates from the second set we have the two sets as:
$\{a,b,c,d,e\}\&\{a,c,d,e\}$
Here, the first set has 5 elements while the second set has 4 elements.
Hence the two sets are neither equal nor equivalent.

$C.\{x:x\text{is a positive multiple of 7}\}$ and $\{7,14,21,28,...\}$
Writing the first set in roster form, we can write it as:
$\{7,14,21,28,...\}\&\{7,14,21,28,...\}$

Hence, the two sets are identical and hence equal which means they are equivalent as well.