Question

let sets a and b be defined as follows.
a = {d, e, f, g, h, i}
b is the set of integers greater than −6 and less than 0
(a) find the cardinalities of a and b.
n(a) =
n(b) =
(b) select true or false.

true

false

m ∉ a | ○ | ○
h ∈ a | ○ | ○
−1 ∈ b | ○ | ○
4 ∈ b | ○ | ○

Explanation:

Step1: Count elements in set A

Count distinct elements: $A=\{d,e,f,g,h,i\}$, so $n(A)=6$.

Step2: Define set B

Integers between -6 and 0: $B=\{-5,-4,-3,-2,-1\}$, so $n(B)=5$.

Step3: Verify $m

otin A$
$m$ is not in $A$, so this is true.

Step4: Verify $h \in A$

$h$ is an element of $A$, so this is true.

Step5: Verify $-1 \in B$

$-1$ is in $B$, so this is true.

Step6: Verify $4 \in B$

$4$ is not in $B$, so this is false.

Answer:

Part (a)

$n(A) = 6$, $n(B) = 5$

Part (b)

Statement	True	False

| $m
otin A$ | $\bigcirc$ | |

$h \in A$	$\bigcirc$
$-1 \in B$	$\bigcirc$
$4 \in B$		$\bigcirc$