Question

let sets a and b be defined as follows. a is the set of integers greater than or equal to −10 and less than or equal to −3 b = {−29, −23, 22, 26, 27, 30} (a) find the cardinalities of a and b. n(a) = n(b) = (b) select true or false. -23 ∈ b -16 ∈ a 28 ∉ b -9 ∈ a

Explanation:

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Part (a)

Step1: List elements of set A

Integers from -10 to -3: $\{-10, -9, -8, -7, -6, -5, -4, -3\}$

Step2: Count elements of A

$n(A) = 8$

Step3: Count elements of set B

$B=\{-29, -23, 22, 26, 27, 30\}$, so $n(B)=6$

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Part (b)

Step1: Check $-23 \in B$

$-23$ is in set $B$: True

Step2: Check $-16 \in A$

$-16 < -10$, not in $A$: False

Step3: Check $28

otin B$
$28$ is not in set $B$: True

Step4: Check $-9 \in A$

$-9$ is in set $A$: True

Answer:

(a) $n(A)=8$, $n(B)=6$
(b)

• $-23 \in B$: True
• $-16 \in A$: False
• $28

otin B$: True

• $-9 \in A$: True