Let a, b and c be the sets: . a={1,3,5,6,8,10} • b = {2,3,6,9} • c = {1,5,7) write these as sets explicitly (list all possible elements enclosed within {}). (a) aub (b) bnc (c) a-b (d) bxc (c) pic).

(a)

(b)

(c)

(d)

(e)

Step-by-step explanation:

Given information:

A, B and C are three sets:

A={1,3,5,6,8,10}, B = {2,3,6,9}, C = {1,5,7}

A set contains distinct elements.

(a)

We need to find the set AUB. In this set all elements of A and B are included.

(b)

We need to find the set B∩C. In this set all common elements of B and C are included.

It is an empty set because there is no common element in set B and C.

(c)

We need to find the set A-B. In this set all elements of A are included excluding the common elements of A and B.

(d)

We need to find the set BxC.

BxC is defined as

(e)

We need to find the set P(C). It is a power set of C. It is the collection of all subsets of set C.

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!