Question

Define the following sets.

A = {x ∈ Z: x is a multiple of 3}

B = {3, 5, 7, 9}

C = {2, 3, 4, 5}

Indicate whether each statement is true or false.

(a)

|B| = |C|

(b)

|A ∩ B| = |A ∩ C|

(c)

A ∩ C ⊆ A ∩ B

(d)

C - B ⊆ A

(e)

B ∪ C = {3, 5}

(f)

2 ∈ A ∪ C

(g)

{2, 3} ∈ C

(h)

{3} ∈ P(C)

(i)

A ∩ B ∩ C = ∅

(j)

∅ ∈ A

Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.

A = {x ∈ Z: x is a multiple of 3}={3,6.9,12,15,.....}

B = {3, 5, 7, 9}

C = {2, 3, 4, 5}

Step 2

a. B = {3, 5, 7, 9}

C = {2, 3, 4, 5}

|B|= number of elements in B= 4

|C|=number of elements in C=4

So, |B|=|C| is true.

Answer(a): True.

Step 3

|A ∩ B|= 2 and |A ∩ C|=1

So b is not ...

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