Question

A={ x:x is a prime number less than 10}
B={x:x is a natural number divides 12}
a. Write A, B in roaster form
b. Find A union and A-B
c. Verify that A union B minus A (A minus B)

Answer 1

hey mate here is ur answer....

in the 3rd part it must be B-A on the right hand side....else it can't be proved.

Answer 2

Answer:

a. A = {$2,3,5,7$}, B = {$1,2,3,4,6,12$}

b. $A$∪$B$ = {$1,2,3,4,5,6,7,12$}, $A-B$ = {$5,7$}

c. Identity doesn't hold.

Step-by-Step Explanation:

a. Roster form: All the elements of sets are listed within the braces { } and are separated by commas is called roster form.

Prime numbers less than $10$ are $2,3,5,7$.

Roster form of A = {$2,3,5,7$}.

Natural numbers that divides $12$ are $1,2,3,4,6,12$.

Roster form of B = {$1,2,3,4,6,12$}.

b. Union: Union of sets A and B is the collection all the elements of A and all the elements of B, common elements are taken only once.

$A-B$ (Difference): The difference of the sets A and B is the set of elements which belong to A but not to B.

Therefore, $A$∪$B$ = {$1,2,3,4,5,6,7,12$}

$A-B$ = {$5,7$}

c. To show: ($A$∪$B$) - $A$ = $A-B$

Compute left hand side as follows:

($A$∪$B$) - $A$ = {$1,4,6,12$}

Compute right hand side as follows:

$A-B$ = {$5,7$}

Notice that  ($A$∪$B$) - $A$ ≠ $A-B$.

But result will hold for $B-A$.

$B-A$ = {$1,4,6,12$}

Thus, ($A$∪$B$) - $A$ = $B-A$.

#SPJ3