Question

use the venn - diagram to the right to determine the following set or cardinality. (a∩b)∪(a∩b) choose the correct answer below, and fill in the answer box to complete your choice. a. the expression (a∩b)∪(a∩b) corresponds to the cardinal number (type a whole number.) b. the expression (a∩b)∪(a∩b) corresponds to the set (use a comma to separate answers as needed.)

Explanation:

Step1: Identify the sets in the Venn - diagram

$A'$ is the complement of set $A$. Elements in $A'$ are those not in circle $A$. $B$ is the set represented by the right - hand circle. $A$ is the set represented by the left - hand circle.

Step2: Find $A'\cap B$

The elements in $A'\cap B$ are the elements that are in $B$ but not in $A$. From the Venn - diagram, the elements in $A'\cap B$ are $\{49\}$.

Step3: Find $A\cap B$

The elements in $A\cap B$ are the elements that are in both $A$ and $B$. From the Venn - diagram, the elements in $A\cap B$ are $\{48,47\}$.

Step4: Find $(A'\cap B)\cup(A\cap B)$

The union of two sets $S_1$ and $S_2$, denoted as $S_1\cup S_2$, is the set of all elements that are in $S_1$ or in $S_2$ (or in both). So, $(A'\cap B)\cup(A\cap B)=\{48,47,49\}$.

Step5: Calculate the cardinality

The cardinality of a set is the number of elements in the set. The set $(A'\cap B)\cup(A\cap B)$ has 3 elements.

Answer:

A. The expression $(A'\cap B)\cup(A\cap B)$ corresponds to the cardinal number 3.