Question 51241
<pre><font size = 5><b>Let S=the solution set for x² = 16.
and T=the solution set for x+2 = 16.
List the elements of each set. 
a.S <font face = "symbol">Ç</font> T b. S <font face = "symbol">È</font> T 

            x² = 16
       x² - 16 = 0
(x - 4)(x + 4) = 0

Set each factor = 0:

Setting x - 4 = 0 gives solution x = 4
Setting x + 4 = 0 gives solution x = -4

So S = {4, -4}

        x + 2 = 16
            x = 14

So T = {14}
            
S <font face = "symbol">È</font> T = {4, -4} <font face = "symbol">È</font> {14}

The union of two sets is the set of every element 
that is either an element of S, an element of T, 
or an element of both sets.

So S <font face = "symbol">È</font> T = {4, -4, 14}

The intersection of two sets is the set of every 
element that is an element of both sets:

S <font face = "symbol">Ç</font> T = {4, -4} <font face = "symbol">Ç</font> {14} = {} or <font face = "symbol">Æ</font>,

that is, the empty or null set, since there are 
no elements that both S and T have in common.

Edwin</pre>