Question

Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10}; B = {2, 3, 5, 7}. Write the set (A U B)’.​

Answer 1

${\huge\red{A}\blue{n}\green{s}\pink{w}\purple{e}\red{r}{\huge{\mathcal{:-}}}}$

Solution:

Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10}; B = {2, 3, 5, 7}

U = { 1, 2, 3, 4, 5, 6, 7, 8, 9}

A = {2, 4, 6, 8}

A U B = {2, 3, 4, 5, 6, 7, 8}

(A U B)’ = {1, 9}

Answer 2

Answer:

The answer for the given problem for finding $(A\cup B)'$ comes out to be $\{1,9\}$

Step-by-step explanation:

The given Universal set, U is defined as:

$U=\{x:x\in N, x\le 9\}$

We can say that the Universal set following the given definition is:

$U=\{1,2,3,4,5,6,7,8,9\}$

Similarly, the given definition of the set A is:

$A=\{x:x \ is \ an \ even \ number\ ,\ 0 < x < 10\}$

We can say that the set A following the given definition is as follows:

$A=\{2,4,6,8\}$

We are given the set B in the problem as follows:

$B=\{2,3,5,7\}$

We know that the expression $(A\cup B)'$ means:

$(A\cup B)'=U-(A\cup B)$

Now that we have both the sets A and B, we can find their union which comes out to be:

$A\cup B=\{2,3,4,5,6,7,8\}$

Now, finding $(A\cup B)'$, we get:

$(A\cup B)'=\{1,2,3,4,5,6,7,8,9\}-\{2,3,4,5,6,7,8\}$

$(A\cup B)'=\{1,9\}$