Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Oct 27, 2023

Find the union of sets A and B given the universal set U. $U=\{1,2,3,4,5,6,7,8\}$ , $A=\{1,2,4,7\}$ , $B=\{5,2,8\}$ C. $A \cup B=\{1,2,4,5,7,8\}$

STEP 1

Assumptions1. The universal set U is $\{1,,3,4,5,6,7,8\}$ . Set A is $\{1,,4,7\}$
3. Set B is $\{5,,8\}$
4. The operation to be performed is union, denoted by $\cup$

STEP 2

The union of two sets A and B is the set of elements which are in A, in B, or in both A and B. We can write this as $A \cup B = \{x x \in A \, or \, x \in B\}$

STEP 3

Now, we will find the union of sets A and B. We start by listing the elements of set A $A \cup B = \{1,2,,7,\ldots\}$

STEP 4

Next, we add the elements of set B that are not already in the union $A \cup B = \{1,2,4,7,,8\}$

STEP 5

We can see that all elements are unique, so we have found the union of sets A and B. We can write this as $A \cup B = \{1,2,4,7,5,8\}$ So, the correct choice is A. $A \cup B=\{1,2,4,7,5,8\}$

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