Question

let sets a and b be defined as follows.
a is the set of integers greater than -7 and less than -2
b = {b, d, e, m, t}
(a) find the cardinalities of a and b.
n(a) =
n(b) =
(b) select true or false.
-6 ∈ a
-14 ∈ a
t ∈ b
= ∉ b

Explanation:

Step1: List elements of set A

Integers greater than $-7$ and less than $-2$ are $-6, -5, -4, -3$.

Step2: Calculate $n(A)$

Count elements of $A$: $n(A) = 4$

Step3: Calculate $n(B)$

Count elements of $B=\{b,d,e,m,t\}$: $n(B) = 5$

Step4: Verify $-6 \in A$

$-6$ is in the list for $A$, so this is True.

Step5: Verify $-14 \in A$

$-14 < -7$, so not in $A$, this is False.

Step6: Verify $t \in B$

$t$ is an element of $B$, so this is True.

Step7: Verify $z

otin B$
$z$ is not in $B$, so this is True.

Answer:

(a) $n(A) = 4$, $n(B) = 5$
(b)

• $-6 \in A$: True
• $-14 \in A$: False
• $t \in B$: True
• $z

otin B$: True