Question

for any two sets a and b, a-b union b-a is equals to:- [a-b] union a, [b-a] union b, [a union b]- [a intersection b}, { a union b} intersection {a intersection b}

Answer 1

Given:

Two sets $a$ and $b$.

To find:

The value of $(a-b)\cup (b-a) = ?$

Options are:

$1.\ (a-b)\cup a\\2.\ (b-a)\cup b\\3.\ (a\cup b) - (a\cap b)\\4.\ (a\cup b) \cap (a\cap b)$

Solution:

First of all, let us understand the meanings of each symbol w.r.to sets.

Minus means the elements of one set which are not in the other set.

Intersection means the common elements between the two sets.

Union means the elements which are present in one set only plus the common elements and the elements present in the second set only. Elements will not be repeated.

Let us solve this by using an example.

Let the sets be:

$a = \{1, 2, 3, 4\}\\b = \{ 2, 4, 7, 8\}$

$a - b = \{1,3\}\\b - a = \{7, 8\}\\(a-b)\cup (b-a) =\{1,3, 7,8\}$

$a \cup b = \{1, 2, 3, 4, 7, 8\}$

$a\cap b = \{2, 4\}$

Now, let us have a look at the options given one by one:

$1.\ (a-b)\cup a = \{1,2, 3, 4\}$

Therefore, not the correct answer.

$2.\ (b-a)\cup b = {2,4,7,8}$

Therefore, not the correct answer.

$3.\ (a\cup b) - (a\cap b) = \{1,2,3,4,7,8\} - \{2, 4\} = \{1, 3, 7, 8\}$

So, it is the correct answer.

$4.\ (a\cup b) \cap (a\cap b) = \{1,2,3,4,7,8\} \cap \{2, 4\} = \{2,4\}$

Therefore, not the correct answer.