Set A has a members and set B has b mmbers. Set C consists of all members that are either set A or set B....?

....with the exception of the x common mmbers (x%26gt;0). Which of the following represents th number of members in set C?





(A) a+b+x


(B) a+b-x


(C) a+b+2x


(D) a+b-2x


(E) 2a+2b+2x





2.) If x = a+z and y=a-z, which of the following represents the product of x and y for every number a and z?





(A) az


(B) z^2


(C) a^2


(D) a^2-z^2


(E) a^2-2az-z^2

Set A has a members and set B has b mmbers. Set C consists of all members that are either set A or set B....?
Hi,





Set A has a members and set B has b members. Set C consists of all members that are either set A or set B....?





....with the exception of the x common members (x%26gt;0). Which of the following represents th number of members in set C?





All of "a" plus all of "b" minus "x" from both groups in the overlap, so they don't get counted.


(A) a+b+x


(B) a+b-x


(C) a+b+2x


(D) a+b-2x %26lt;== ANSWER


(E) 2a+2b+2x





2.) If x = a+z and y=a-z, which of the following represents the product of x and y for every number a and z?





product of x and y = xy = (a + z)(a - z) = a² - z²





(A) az


(B) z^2


(C) a^2


(D) a^2-z^2 %26lt;== ANSWER


(E) a^2-2az-z^2





I hope that helps!! :-)
Reply:B) a+b-x





E)a^2-2az-z^2
Reply:1):D


The number of members in total in A and B is a+b-x


The number of members not including the common members is a+b-2x








2):D
Reply:1) C will have all the members of A and of B without the common members. However the common members are counted twice in considering A and B. Thus, the number of members in set C will be a + b - 2x. (D)





2) D. This is elementary algebraic expansion.

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