Question

can u pls tell me how to solve this ?​

Answer 1

Answer:

It is true that (A∪B)$-$(A∩B)$=$(A$-$B)∪(B$-$A) $=\{0,1/2,1,3/2,2,5/2,7/2,5}$$\}$

Step-by-step explanation:

To solve this question you have to find the sets A and B first of all.

Then find the sets A∪B, A∩B, A$-$B, and B$-$A. Finally verify the given equation.

Here A is the set of all integers in between $-\frac{1}{2}\ and\ \frac{9}{2}$ , excluding the numbers $-\frac{1}{2}\ and\ \frac{9}{2}$, that is what is meant by $-\frac{1}{2}\ <\ x<\ \frac{9}{2}$.

Therefore $A=\{0,\frac{1}{2},\ \frac{2}{2},\ \frac{3}{2},\ \frac{4}{2} ,\ \frac{5}{2},\ \frac{6}{2} ,\ \frac{7}{2},\ \frac{8}{2} \}$

That is $A=\{0,\frac{1}{2} , 1,\frac{3}{2} , 2, \frac{5}{2} , 3, \frac{7}{2}, 4\}$

And, B is the set of natural numbers in between $2$ and $5$, excluding $2$ and including $5$ . That is what is meant by $2<x$ ≤ $5$ .

Therefore $B=\{3,4,5\}$ .

Now A∪B is the set of all elements in A and B

Therefore A∪B $=\{0,1/2,1,3/2,2,5/2,3,7/2,4,5\}$.

A∩B is the set of elements in both A and B .

That is A∩B $=\{3,4\}$ .

Thus (A∪B) $-$ (A∩B) $=\{0,1/2,1,3/2,2,5/2,7/2,5\}$ . . . . (1)

Next,

$A-B= \{0,1/2,1,3/2,2,5/2,3,7/2,4\}-\{3,4,5\}$

          $=\{0,1/2,1,3/2,2,5/2,7/2\}$

$B-A=\{3,4,5\}-\{0,1/2,1,3/2,2,5/2,3,7/2,4\}$

          $=\{5\}$

Therefore ,

($A-B$) ∪ ($B-A$) $=\{0,1/2,1,3/2,2,5/2,7/2,5\}$ . . . . (2)

From (1)and (2) it is obvious that

(A∪B)$-$(A∩B)$=$(A$-$B)∪(B$-$A)

Hence the answer.

thank you