need math help. can some one answer this problem.?

Question

given that U = {a, b, c, d, e, f, g, h}
A = {a, b, d, e}B = {b, c, e, f}
what is A ∩ B? can some one explain it. the book is confusing.

also what is the diffrence between B ∩ Aand A ∩ Bor is there any diffrence?

Answer 1

A intersection B - those would be the elements that A and B share in common. In this case, it would be {b, e}. This is as opposed to the union, which would be the set with all of the elements in either A or B.

Edit: In this sense, intersection is commutative.

Answer 2

Before we talk about what unions and intersections are, let's look at the context in which we use unions and intersections. We usually use them when talking about SETS. A set is really just a collection of objects, numbers, or whatever. For instance, the natural numbers are a set. Or, A in your example is a set.

If we have two sets, A and B, then the union of A and B is notated: A U B. A U B is a new set whose elements are the elements of both A and B. So, if something is an element of either A or B, it is also an element of A U B. Suppose we have the sets: A = {real numbers xlx>0} (so, this is just the positive real numbers) and B = {yl y is an integer}. Then, A U B would be the set of positive real numbers and negative integers (0 is included).

Now, the INTERSECTION of A and B is a little different. The usual notation for intersection is kind of an upside down U. If you take the union sign and flip it, you will get the intersection sign. But, since there is no such sign on the keyboard, I will use "i" to signify intersection. So A i B is a new set whose elements are in both A and B. So, in the example above, A i B would be the set of all positive real integers since positive real integers are in A (they are positive real numbers) and they are also in B (they are integers). Sometimes two sets have no elements in common. Then the intersection of the two sets is called the empty set, often denoted {}. For instance, if C = {1, 3, 5, ...} and D = {2, 4, 6, ...}, then C i D = {}.

Let me just give one more example on a more finite level that might make things clearer. Suppose you have the following two sets:
K={0,1,2,3,6,8}
F={-1, 2, 3, 7/2, 8}

Then K U F is the set of all numbers that are in either K or F.
So, K U F = {0,1,2,3,6,8,-1,7/2}

K i F is the set of all numbers that are in both K and F.
So, K i F = {2,3,8}

In your case, find all the values that are in BOTH A and B

Answer 3

The symbol ∩ means 'intersection'. Like where two roads meet, there is a common piece that they share.

So what is the common piece shared between A and B? Which elements do they both have?

b and e, of course. You'd write this as a set, though - {b, e}.

U is irrelevant for this question. It is the 'universal set', or the set that contains everything in the 'universe' of this question. It would only be useful for questions such as 'What is NOT in A?' Answer { c, f, g, h }.

[I missed your second question at first: A ∩ B is equal to B ∩ A. That is one of the properties of this symbol that can be proved but it is actually fairly obvious. In plain English, you'd say "The things that A has in common with B are the same as the things that B has in common with A".]

Answer 4

i think the upside-down U means "and" in logic. so A ∩ B would be everything in subset A and B.

think of a Venn diagram (the diagram with 2 overlapping circles) and the answer beingwhat is in the overlapping part.