A X (B U C) how do I set this problem up Math?

Question

A = A, B, C B = C, D, E C = A, C, X

A X (B interesection sign C)

How would I go about solving this? The solution given was (A,C) (B,C) and (C,C)

I didn't get the same.

By the way the U symbol is upside down - intersection but did not know how do this on keyboard.

Answer 1

B={C, D, E}

C={A, C, X}

The intersection of B and C is {C} since it is the only common element (which is the definition of intersection).

So:

A={A,B,C}

B∩C={C}

A×{C}={(A,C), (B,C), (C,C)} since set multiplication is distributive.



Thus:

A×(B∩C)=A×{C}={(A,C), (B,C), (C,C)}

Answer 2

First, it's rather confusing that you use the same letters (A, B, C) to denote sets and elements of sets, and also the same letter (X) to denote an element as well as the cartesian product (especially since you do not put elements between curly brackets {..}).



Second A = A, B, C B = C, D, E C = A, C, X made no sense at first

However, A = {A, B, C}, B = {C, D, E}, C = {A, C, X} is much easier to make sense of.



In math, it's very important to use proper symbols, or you'll lose marks on your work.



Leaving aside my concerns:

B ∩ C = {C, D, E} ∩ {A, C, X} = {C}



A x (B ∩ C) = {A, B, C} x {C} = {(A,C), (B,C), (C,C)}

Answer 3

Buc Math

Answer 4

you really shouldn't use the same letters for elements of a set, and the set itself. it's confusing.



if A = {a,b,c}, B = {c,d,e} and C = {a,c,x}



then A x (B ∩ C) is all possible pairs of elements of A and elements of B ∩ C.



so first we have to identifiy B ∩ C, which is all elements common to both B and C.



in this case B ∩ C = {c}



so the possible pairs in A x (B ∩ C) are (a,c), (b,c) and (c,c) so



A x (B ∩ C) = {(a,c),(b,c),(c,c)}