Find the following then use diagram to illustrate each 1. P ∪ R
P = { 1,3,5,7,9,11,13...21 }
R = { 2,4,6,8,10,12 }

2. P ∪ ( R ∪ O )
P = { 1,3,5,7,9,11,13...21 }
R = { 2,4,6,8,10,12 }
O = { 3, 6, 9, 12, 15, 18 }

3. ( O ∩ V ) ∩ E
O = { 3, 6, 9, 12, 15, 18 }
V = { 4,16,20 }
E = { 5, 10, 15, 20 }

thank you

Step-by-step explanation:

I hope you have find your answer and i haven't done number 3 because nothing is common between O and V so its answer is 0 hope this make your day my friend

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.