Question

1. set a = {m, s, n, o, r, m, a, n} and set b = {m, a, t, h}. what is set a and b
2. set a {5, 10, 15, 20, 25} and set b {10, 20, 30, 40, 50}

a - what is set a and b
b - what is set a or b
c - if set a and b have subsets c and d and subset c is {10, 30, 50} and subset d has none of the elements of subset c what elements does subset d contain?

1. what is the symbol for and in probability?
2. what is the symbol for or in probability?

Explanation:

Step1: Find intersection of sets in 15

Intersection is common elements.
$A\cap B = \{M, A\}$

Step2: Find intersection of sets in 16 - a

Common elements in $A = \{5, 10, 15, 20, 25\}$ and $B=\{10, 20, 30, 40, 50\}$.
$A\cap B=\{10, 20\}$

Step3: Find union of sets in 16 - b

Union is all unique elements.
$A\cup B = \{5, 10, 15, 20, 25, 30, 40, 50\}$

Step4: Find elements of subset D in 16 - c

$A\cup B=\{5, 10, 15, 20, 25, 30, 40, 50\}$, $C = \{10, 30, 50\}$.
Elements in $A\cup B$ not in $C$ are $\{5, 15, 20, 25, 40\}$, so $D=\{5, 15, 20, 25, 40\}$

Step5: Symbol for and in probability in 17

The symbol for and in probability is $\cap$.

Step6: Symbol for or in probability in 18

The symbol for or in probability is $\cup$.

Answer:

1. $A\cap B = \{M, A\}$

16 - a. $A\cap B=\{10, 20\}$
16 - b. $A\cup B = \{5, 10, 15, 20, 25, 30, 40, 50\}$
16 - c. $D=\{5, 15, 20, 25, 40\}$

1. $\cap$
2. $\cup$