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.

	true	false
( -16 in a )

| ( 28
otin b ) | | |

( -9 in a )

Explanation:

Step1: List set A elements

$A = \{-10, -9, -8, -7, -6, -5, -4, -3\}$

Step2: Count A's cardinality

$n(A) = 8$

Step3: Count B's cardinality

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

Step4: Verify $-23 \in B$

$-23$ is in $B$ → True

Step5: Verify $-16 \in A$

$-16 < -10$, not in $A$ → False

Step6: Verify $28

otin B$
$28$ is not in $B$ → True

Step7: Verify $-9 \in A$

$-9$ is in $A$ → True (corrected from original false selection)

Answer:

Part (a)

$n(A)=8$, $n(B)=5$

Part (b)

Statement	True	False
$-16 \in A$	$\circ$	$\odot$

| $28
otin B$ | $\odot$ | $\circ$ |

$-9 \in A$

$\circ$

$\odot$