Determine whether each of these pairs of sets are equal. (1 pt each) a) {1,3,3,3,5,5,5,5,5}, {5,3,1} b) {{1}}, {1,{1}} c) ∅, {∅}

$a) \{1,3,3,3,5,5,5,5,5\}, \{5,3,1\}$

The two sets are equal.

We need to look only at the distinct elements, not the repetitions or the order. The two sets contains common elements 1, 3 and 5.

Hence, they are equal.

$b) \{\{1\}\}, \{1,\{1\}\}$

If the two sets are equal then the cardinality of the sets are same.

But, $|\{\{1\}\}|=1\ and \ |\{1,\{1\}\}|=2$

So, $\{\{1\}\}$ and $\{1,\{1\}\}$ are not same.

$c) \phi, \{\phi\}$

Not same

$|\phi|=0$ but $|\{\phi\}|=1$

So, $\phi$ and $\{\phi\}$ are not same.